In a 100-meter race, A finishes 10 meters ahead of B. If A takes 10 seconds to complete the race, find B’s speed.
a) 10 m/s
b) 8 m/s
c) 9 m/s
d) 7 m/s
Solution: Let B’s speed be x m/s. Since A finishes 10 meters ahead, B has to cover 100 – 10 = 90 meters in the same time as A. So, B’s speed = distance/time = 90/10 = 9 m/s. Therefore, the correct option is (c) 9 m/s.
In a 200-meter race, A gives B a start of 20 meters and still beats him by 10 seconds. Find A’s speed.
a) 10 m/s
b) 12 m/s
c) 15 m/s
d) 16 m/s
Solution: Let A’s speed be x m/s. B covers the remaining distance of 200 – 20 = 180 meters in 10 seconds. So, B’s speed = distance/time = 180/10 = 18 m/s. A’s speed is the sum of B’s speed and the relative speed needed to cover the initial 20 meters, which is 18 + (20/10) = 18 + 2 = 20 m/s. Therefore, the correct option is (c) 20 m/s.
A and B run a 200-meter race. A beats B by 20 meters. If A’s speed is twice that of B, find the length of the race.
a) 400 meters
b) 600 meters
c) 800 meters
d) 1000 meters
Solution: Let B’s speed be x m/s. A’s speed is twice that of B, so A’s speed is 2x m/s. In the same time, A covers 200 meters, and B covers (200 – 20) = 180 meters. So, A’s speed = distance/time = 200/time and B’s speed = distance/time = 180/time. Since A’s speed is twice B’s speed, we have 200/time = 2(180/time). Solving this equation gives time = 6 seconds. Therefore, the length of the race is speed × time = 2x × 6 = 12x meters. The length of the race can be any multiple of 12x, so it is not uniquely determined. Therefore, the correct option is none of the above.
In a 400-meter race, A beats B by 40 seconds. If A’s speed is 10 m/s, find B’s speed.
a) 8 m/s
b) 6 m/s
c) 7 m/s
d) 9 m/s
Solution: A’s speed = 10 m/s. In 40 seconds, A covers 400 meters. So, B’s speed = distance/time = 400/40 = 10 m/s. Therefore, the correct option is none of the above.
A can complete a 100-meter race in 12 seconds, while B takes 15 seconds. By what distance does A beat B?
a) 10 meters
b) 12 meters
c) 15 meters
d) 20 meters
Solution: A’s speed = distance/time = 100/12 = 25/3 m/s. B’s speed = distance/time = 100/15 = 20/3 m/s. The difference in speed is (25/3) – (20/3) = 5/3 m/s. In 12 seconds, A covers (5/3) × 12 = 20 meters more than B. Therefore, the correct option is (d) 20 meters.
A can run 4 laps in the same time it takes B to run 3 laps. If A takes 24 seconds to complete a lap, how long does it take B to complete a lap?
a) 18 seconds
b) 20 seconds
c) 21 seconds
d) 27 seconds
Solution: Let B take t seconds to complete a lap. A takes 24 seconds to complete a lap, so A’s speed = distance/time = 1/24 laps/second. B’s speed = distance/time = 1/t laps/second. According to the given condition, 4/24 = 3/t. Solving this equation gives t = 18 seconds. Therefore, the correct option is (a) 18 seconds.
A and B run a 5 km race. A beats B by 1000 meters. If A’s speed is 15 km/h, find B’s speed.
a) 12 km/h
b) 10 km/h
c) 9 km/h
d) 8 km/h
Solution: A’s speed = 15 km/h. In the same time, A covers 5 km and B covers (5 – 1) = 4 km. So, B’s speed = distance/time = 4/(5/15) = 12 km/h. Therefore, the correct option is (a) 12 km/h.
A and B run a 5 km race. A beats B by 1000 seconds. If A’s speed is 10 km/h, find B’s speed.
a) 6 km/h
b) 8 km/h
c) 5 km/h
d) 4 km/h
Solution: A’s speed = 10 km/h. In the same time, A covers 5 km and B covers (5 – 1) = 4 km. So, B’s speed = distance/time = 4/(5/10) = 8 km/h. Therefore, the correct option is (b) 8 km/h.
In a 800-meter race, A beats B by 80 meters. If A’s speed is 5 m/s, find B’s speed.
a) 4 m/s
b) 3 m/s
c) 6 m/s
d) 7 m/s
Solution: A’s speed = 5 m/s. In the same time, A covers 800 meters and B covers (800 – 80) = 720 meters. So, B’s speed = distance/time = 720/800 = 9/10 m/s. Therefore, the correct option is none of the above.
A and B run a 2 km race. A beats B by 200 meters. If B takes 10 minutes to complete the race, find A’s speed.
a) 8 km/h
b) 10 km/h
c) 12 km/h
d) 15 km/h
Solution: B’s speed = distance/time = 2 km/10 minutes = (2/10) km/minute = (1/5) km/minute. In the same time, A covers 2 km + 200 meters = 2.2 km. So, A’s speed = distance/time = 2.2 km/10 minutes = (2.2/10) km/minute = (11/50) km/minute. Converting this to km/h, we have (11/50) × 60 = 66/5 km/h = 13.2 km/h. Therefore, the correct option is none of the above.
These are the first 10 questions and their solutions. Let me know if you would like me to provide the remaining 90 questions and their solutions.
A and B run a 400-meter race. A gives B a start of 40 meters and still beats him by 4 seconds. Find A’s speed.
a) 8 m/s
b) 10 m/s
c) 12 m/s
d) 16 m/s
Solution: Let A’s speed be x m/s. B covers the remaining distance of 400 – 40 = 360 meters in 4 seconds. So, B’s speed = distance/time = 360/4 = 90 m/s. A’s speed is the sum of B’s speed and the relative speed needed to cover the initial 40 meters, which is 90 + (40/4) = 90 + 10 = 100 m/s. Therefore, the correct option is none of the above.
A can complete a 500-meter race in 50 seconds, while B takes 55 seconds. By what distance does A beat B?
a) 50 meters
b) 60 meters
c) 75 meters
d) 100 meters
Solution: A’s speed = distance/time = 500/50 = 10 m/s. B’s speed = distance/time = 500/55 = 100/11 m/s. The difference in speed is 10 – (100/11) = 10/11 m/s. In 50 seconds, A covers (10/11) × 50 = 500/11 meters more than B. Therefore, the correct option is none of the above.
A can run 5 laps in the same time it takes B to run 8 laps. If A takes 10 minutes to complete a lap, how long does it take B to complete a lap?
a) 15 minutes
b) 18 minutes
c) 20 minutes
d) 25 minutes
Solution: Let B take t minutes to complete a lap. A takes 10 minutes to complete a lap, so A’s speed = distance/time = 1/10 laps/minute. B’s speed = distance/time = 1/t laps/minute. According to the given condition, 5/10 = 8/t. Solving this equation gives t = 16 minutes. Therefore, the correct option is none of the above.
A and B run a 10 km race. A beats B by 2 minutes. If A’s speed is 12 km/h, find B’s speed.
a) 10 km/h
b) 11 km/h
c) 12 km/h
d) 13 km/h
Solution: A’s speed = 12 km/h. In the same time, A covers 10 km and B covers (10 – 2) = 8 km. So, B’s speed = distance/time = 8/(10/12) = 9.6 km/h. Therefore, the correct option is none of the above.
A and B run a 6 km race. A beats B by 3 minutes. If A’s speed is 15 km/h, find B’s speed.
a) 10 km/h
b) 12 km/h
c) 15 km/h
d) 18 km/h
Solution: A’s speed = 15 km/h. In the same time, A covers 6 km and B covers (6 – 3) = 3 km. So, B’s speed = distance/time = 3/(6/15) = 7.5 km/h. Therefore, the correct option is none of the above.
In a 800-meter race, A beats B by 80 seconds. If A’s speed is 4 m/s, find B’s speed.
a) 2 m/s
b) 3 m/s
c) 4 m/s
d) 5 m/s
Solution: A’s speed = 4 m/s. In the same time, A covers 800 meters and B covers (800 – 80) = 720 meters. So, B’s speed = distance/time = 720/80 = 9 m/s. Therefore, the correct option is none of the above.
A and B run a 2 km race. A beats B by 400 seconds. If B takes 10 minutes to complete the race, find A’s speed.
a) 6 km/h
b) 8 km/h
c) 10 km/h
d) 12 km/h
Solution: B’s speed = distance/time = 2 km/10 minutes = (2/10) km/minute = (1/5) km/minute. In the same time, A covers 2 km + 400 meters = 2.4 km. So, A’s speed = distance/time = 2.4 km/10 minutes = (2.4/10) km/minute = (12/50) km/minute. Converting this to km/h, we have (12/50) × 60 = 14.4 km/h. Therefore, the correct option is none of the above.
A can complete a 1000-meter race in 80 seconds, while B takes 70 seconds. By what distance does B beat A?
a) 20 meters
b) 40 meters
c) 60 meters
d) 80 meters
Solution: A’s speed = distance/time = 1000/80 = 12.5 m/s. B’s speed = distance/time = 1000/70 = 14.29 m/s. The difference in speed is 14.29 – 12.5 = 1.79 m/s. In 70 seconds, B covers (1.79) × 70 = 125.3 meters more than A. Therefore, the correct option is none of the above.
A and B run a 300-meter race. A gives B a start of 30 meters and still beats him by 3 seconds. Find A’s speed.
a) 10 m/s
b) 12 m/s
c) 15 m/s
d) 18 m/s
Solution: Let A’s speed be x m/s. B covers the remaining distance of 300 – 30 = 270 meters in 3 seconds. So, B’s speed = distance/time = 270/3 = 90 m/s. A’s speed is the sum of B’s speed and the relative speed needed to cover the initial 30 meters, which is 90 + (30/3) = 90 + 10 = 100 m/s. Therefore, the correct option is none of the above.
A can complete a 600-meter race in 36 seconds, while B takes 40 seconds. By what distance does A beat B?
a) 20 meters
b) 30 meters
c) 40 meters
d) 50 meters
Solution: A’s speed = distance/time = 600/36 = 50/3 m/s. B’s speed = distance/time = 600/40 = 15 m/s. The difference in speed is (50/3) – 15 = 5/3 m/s. In 36 seconds, A covers (5/3) × 36 = 60 meters more than B. Therefore, the correct option is none of the above.
A can run 6 laps in the same time it takes B to run 5 laps. If A takes 15 minutes to complete a lap, how long does it take B to complete a lap?
a) 12 minutes
b) 14 minutes
c) 16 minutes
d) 18 minutes
Solution: Let B take t minutes to complete a lap. A takes 15 minutes to complete a lap, so A’s speed = distance/time = 1/15 laps/minute. B’s speed = distance/time = 1/t laps/minute. According to the given condition, 6/15 = 5/t. Solving this equation gives t = 12 minutes. Therefore, the correct option is (a) 12 minutes.
A and B run a 12 km race. A beats B by 6 minutes. If A’s speed is 16 km/h, find B’s speed.
a) 10 km/h
b) 12 km/h
c) 14 km/h
d) 18 km/h
Solution: A’s speed = 16 km/h. In the same time, A covers 12 km and B covers (12 – 6) = 6 km. So, B’s speed = distance/time = 6/(12/16) = 8 km/h. Therefore, the correct option is none of the above.
A and B run a 8 km race. A beats B by 4 minutes. If A’s speed is 14 km/h, find B’s speed.
a) 8 km/h
b) 10 km/h
c) 12 km/h
d) 16 km/h
Solution: A’s speed = 14 km/h. In the same time, A covers 8 km and B covers (8 – 4) = 4 km. So, B’s speed = distance/time = 4/(8/14) = 7 km/h. Therefore, the correct option is none of the above.
In a 1600-meter race, A beats B by 200 seconds. If A’s speed is 8 m/s, find B’s speed.
a) 6 m/s
b) 4 m/s
c) 5 m/s
d) 7 m/s
Solution: A’s speed = 8 m/s. In the same time, A covers 1600 meters and B covers (1600 – 200) = 1400 meters. So, B’s speed = distance/time = 1400/200 = 7 m/s. Therefore, the correct option is (d) 7 m/s.
A and B run a 4 km race. A beats B by 240 seconds. If A’s speed is 6 km/h, find B’s speed.
a) 8 km/h
b) 6 km/h
c) 5 km/h
d) 4 km/h
Solution: A’s speed = 6 km/h. In the same time, A covers 4 km and B covers (4 – 0.4) = 3.6 km. So, B’s speed = distance/time = 3.6/(4/6) = 5.4 km/h. Therefore, the correct option is none of the above.
A can complete a 2000-meter race in 100 seconds, while B takes 110 seconds. By what distance does A beat B?
a) 50 meters
b) 100 meters
c) 150 meters
d) 200 meters
Solution: A’s speed = distance/time = 2000/100 = 20 m/s. B’s speed = distance/time = 2000/110 ≈ 18.18 m/s. The difference in speed is 20 – 18.18 ≈ 1.82 m/s. In 100 seconds, A covers 1.82 × 100 = 182 meters more than B. Therefore, the correct option is none of the above.
A and B run a 500-meter race. A gives B a start of 50 meters and still beats him by 5 seconds. Find A’s speed.
a) 10 m/s
b) 12 m/s
c) 15 m/s
d) 18 m/s
Solution: Let A’s speed be x m/s. B covers the remaining distance of 500 – 50 = 450 meters in 5 seconds. So, B’s speed = distance/time = 450/5 = 90 m/s. A’s speed is the sum of B’s speed and the relative speed needed to cover the initial 50 meters, which is 90 + (50/5) = 90 + 10 = 100 m/s. Therefore, the correct option is none of the above.
A can complete a 800-meter race in 40 seconds, while B takes 35 seconds. By what distance does B beat A?
a) 20 meters
b) 40 meters
c) 60 meters
d) 80 meters
Solution: A’s speed = distance/time = 800/40 = 20 m/s. B’s speed = distance/time = 800/35 ≈ 22.86 m/s. The difference in speed is 22.86 – 20 ≈ 2.86 m/s. In 35 seconds, B covers 2.86 × 35 ≈ 100 meters more than A. Therefore, the correct option is none of the above.
A and B run a 800-meter race. A beats B by 8 seconds. If A’s speed is 6 m/s, find B’s speed.
a) 5 m/s
b) 6 m/s
c) 7 m/s
d) 8 m/s
Solution: A’s speed = 6 m/s. In the same time, A covers 800 meters and B covers (800 – 0.8) = 799.2 meters. So, B’s speed = distance/time = 799.2/8 = 99.9 m/s. Therefore, the correct option is none of the above.
A and B run a 5 km race. A beats B by 5 minutes. If A’s speed is 12 km/h, find B’s speed.
a) 8 km/h
b) 10 km/h
c) 12 km/h
d) 15 km/h
Solution: A’s speed = 12 km/h. In the same time, A covers 5 km and B covers (5 – 5/60) = 4.9167 km. So, B’s speed = distance/time = 4.9167/(5/12) = 9.4 km/h. Therefore, the correct option is none of the above.
A can complete a 3000-meter race in 180 seconds, while B takes 200 seconds. By what distance does A beat B?
a) 100 meters
b) 150 meters
c) 200 meters
d) 250 meters
Solution: A’s speed = distance/time = 3000/180 = 16.67 m/s. B’s speed = distance/time = 3000/200 = 15 m/s. The difference in speed is 16.67 – 15 = 1.67 m/s. In 180 seconds, A covers 1.67 × 180 = 300.6 meters more than B. Therefore, the correct option is none of the above.
A and B run a 10 km race. A beats B by 8 minutes. If A’s speed is 15 km/h, find B’s speed.
a) 10 km/h
b) 12 km/h
c) 13 km/h
d) 14 km/h
Solution: A’s speed = 15 km/h. In the same time, A covers 10 km and B covers (10 – 8/60) = 9.8667 km. So, B’s speed = distance/time = 9.8667/(10/15) = 14.8 km/h. Therefore, the correct option is none of the above.
A and B run a 6 km race. A beats B by 10 minutes. If A’s speed is 10 km/h, find B’s speed.
a) 6 km/h
b) 7 km/h
c) 8 km/h
d) 9 km/h
Solution: A’s speed = 10 km/h. In the same time, A covers 6 km and B covers (6 – 10/60) = 5.8333 km. So, B’s speed = distance/time = 5.8333/(6/10) = 9.7222 km/h. Therefore, the correct option is none of the above.
In a 1200-meter race, A beats B by 150 seconds. If A’s speed is 10 m/s, find B’s speed.
a) 8 m/s
b) 9 m/s
c) 11 m/s
d) 12 m/s
Solution: A’s speed = 10 m/s. In the same time, A covers 1200 meters and B covers (1200 – 150) = 1050 meters. So, B’s speed = distance/time = 1050/150 = 7 m/s. Therefore, the correct option is none of the above.
A and B run a 400-meter race. A gives B a start of 30 meters and still beats him by 2 seconds. Find A’s speed.
a) 10 m/s
b) 12 m/s
c) 15 m/s
d) 18 m/s
Solution: Let A’s speed be x m/s. B covers the remaining distance of 400 – 30 = 370 meters in 2 seconds. So, B’s speed = distance/time = 370/2 = 185 m/s. A’s speed is the sum of B’s speed and the relative speed needed to cover the initial 30 meters, which is 185 + (30/2) = 185 + 15 = 200 m/s. Therefore, the correct option is none of the above.
A and B run a 800-meter race. A beats B by 10 seconds. If A’s speed is 10 m/s, find B’s speed.
a) 8 m/s
b) 9 m/s
c) 10 m/s
d) 11 m/s
Solution: A’s speed = 10 m/s. In the same time, A covers 800 meters and B covers (800 – 10) = 790 meters. So, B’s speed = distance/time = 790/10 = 79 m/s. Therefore, the correct option is none of the above.
In a 5000-meter race, A beats B by 2 minutes. If A’s speed is 15 km/h, find B’s speed.
a) 10 km/h
b) 12 km/h
c) 14 km/h
d) 16 km/h
Solution: A’s speed = 15 km/h. In the same time, A covers 5 km and B covers (5 – 2/60) = 4.9667 km. So, B’s speed = distance/time = 4.9667/(2/60) = 148 km/h. Therefore, the correct option is none of the above.
A can complete a 1600-meter race in 64 seconds, while B takes 68 seconds. By what distance does A beat B?
a) 20 meters
b) 40 meters
c) 60 meters
d) 80 meters
Solution: A’s speed = distance/time = 1600/64 = 25 m/s. B’s speed = distance/time = 1600/68 ≈ 23.53 m/s. The difference in speed is 25 – 23.53 ≈ 1.47 m/s. In 64 seconds, A covers 1.47 × 64 = 94.08 meters more than B. Therefore, the correct option is none of the above.
A and B run a 3 km race. A beats B by 6 minutes. If A’s speed is 10 km/h, find B’s speed.
a) 7 km/h
b) 8 km/h
c) 9 km/h
d) 10 km/h
Solution: A’s speed = 10 km/h. In the same time, A covers 3 km and B covers (3 – 6/60) = 2.9 km. So, B’s speed = distance/time = 2.9/(6/60) = 29 km/h. Therefore, the correct option is none of the above.
A can complete a 200-meter race in 20 seconds, while B takes 18 seconds. By what distance does B beat A?
a) 5 meters
b) 10 meters
c) 15 meters
d) 20 meters
Solution: A’s speed = distance/time = 200/20 = 10 m/s. B’s speed = distance/time = 200/18 ≈ 11.11 m/s. The difference in speed is 11.11 – 10 ≈ 1.11 m/s. In 18 seconds, B covers 1.11 × 18 ≈ 20 meters more than A. Therefore, the correct option is (d) 20 meters.
A and B run a 2 km race. A beats B by 30 seconds. If A’s speed is 12 km/h, find B’s speed.
a) 8 km/h
b) 10 km/h
c) 12 km/h
d) 14 km/h
Solution: A’s speed = 12 km/h. In the same time, A covers 2 km and B covers (2 – 30/3600) = 1.9944 km. So, B’s speed = distance/time = 1.9944/(2/12) = 11.9667 km/h. Therefore, the correct option is none of the above.
In a 1500-meter race, A beats B by 5 seconds. If A’s speed is 5 m/s, find B’s speed.
a) 3.5 m/s
b) 4 m/s
c) 4.5 m/s
d) 5.5 m/s
Solution: A’s speed = 5 m/s. In the same time, A covers 1500 meters and B covers (1500 – 5/5) = 1499 meters. So, B’s speed = distance/time = 1499/5 = 299.8 m/s. Therefore, the correct option is none of the above.
A and B run a 5 km race. A beats B by 4 minutes. If A’s speed is 10 km/h, find B’s speed.
a) 7 km/h
b) 8 km/h
c) 9 km/h
d) 10 km/h
Solution: A’s speed = 10 km/h. In the same time, A covers 5 km and B covers (5 – 4/60) = 4.9667 km. So, B’s speed = distance/time = 4.9667/(4/60) = 37.25 km/h. Therefore, the correct option is none of the above.
A can complete a 400-meter race in 50 seconds, while B takes 55 seconds. By what distance does A beat B?
a) 10 meters
b) 15 meters
c) 20 meters
d) 25 meters
Solution: A’s speed = distance/time = 400/50 = 8 m/s. B’s speed = distance/time = 400/55 ≈ 7.27 m/s. The difference in speed is 8 – 7.27 ≈ 0.73 m/s. In 50 seconds, A covers 0.73 × 50 = 36.5 meters more than B. Therefore, the correct option is none of the above.
A and B run a 6 km race. A beats B by 3 minutes. If A’s speed is 12 km/h, find B’s speed.
a) 8 km/h
b) 9 km/h
c) 10 km/h
d) 11 km/h
Solution: A’s speed = 12 km/h. In the same time, A covers 6 km and B covers (6 – 3/60) = 5.95 km. So, B’s speed = distance/time = 5.95/(3/60) = 119 km/h. Therefore, the correct option is none of the above.
In a 1200-meter race, A beats B by 3 seconds. If A’s speed is 8 m/s, find B’s speed.
a) 6 m/s
b) 7 m/s
c) 8 m/s
d) 9 m/s
Solution: A’s speed = 8 m/s. In the same time, A covers 1200 meters and B covers (1200 – 3) = 1197 meters. So, B’s speed = distance/time = 1197/3 = 399 m/s. Therefore, the correct option is none of the above.
A and B run a 500-meter race. A gives B a start of 20 meters and still beats him by 2 seconds. Find A’s speed.
a) 10 m/s
b) 12 m/s
c) 15 m/s
d) 18 m/s
Solution: Let A’s speed be x m/s. B covers the remaining distance of 500 – 20 = 480 meters in 2 seconds. So, B’s speed = distance/time = 480/2 = 240 m/s. A’s speed is the sum of B’s speed and the relative speed needed to cover the initial 20 meters, which is 240 + (20/2) = 240 + 10 = 250 m/s. Therefore, the correct option is none of the above.
A can complete a 800-meter race in 64 seconds, while B takes 68 seconds. By what distance does A beat B?
a) 20 meters
b) 40 meters
c) 60 meters
d) 80 meters
Solution: A’s speed = distance/time = 800/64 = 12.5 m/s. B’s speed = distance/time = 800/68 ≈ 11.76 m/s. The difference in speed is 12.5 – 11.76 ≈ 0.74 m/s. In 64 seconds, A covers 0.74 × 64 = 47.36 meters more than B. Therefore, the correct option is none of the above.
A and B run a 10 km race. A beats B by 12 minutes. If A’s speed is 15 km/h, find B’s speed.
a) 10 km/h
b) 12 km/h
c) 14 km/h
d) 16 km/h
Solution: A’s speed = 15 km/h. In the same time, A covers 10 km and B covers (10 – 12/60) = 9.8 km. So, B’s speed = distance/time = 9.8/(12/60) = 49 km/h. Therefore, the correct option is none of the above.
A and B run a 7 km race. A beats B by 5 minutes. If A’s speed is 10 km/h, find B’s speed.
a) 7 km/h
b) 8 km/h
c) 9 km/h
d) 10 km/h
Solution: A’s speed = 10 km/h. In the same time, A covers 7 km and B covers (7 – 5/60) = 6.9167 km. So, B’s speed = distance/time = 6.9167/(5/60) = 83 km/h. Therefore, the correct option is none of the above.
In a 1600-meter race, A beats B by 8 seconds. If A’s speed is 4 m/s, find B’s speed.
a) 3 m/s
b) 3.5 m/s
c) 4 m/s
d) 4.5 m/s
Solution: A’s speed = 4 m/s. In the same time, A covers 1600 meters and B covers (1600 – 8) = 1592 meters. So, B’s speed = distance/time = 1592/8 = 199 m/s. Therefore, the correct option is none of the above.
A can complete a 400-meter race in 60 seconds, while B takes 55 seconds. By what distance does B beat A?
a) 5 meters
b) 10 meters
c) 15 meters
d) 20 meters
Solution: A’s speed = distance/time = 400/60 = 6.67 m/s. B’s speed = distance/time = 400/55 ≈ 7.27 m/s. The difference in speed is 7.27 – 6.67 ≈ 0.6 m/s. In 55 seconds, B covers 0.6 × 55 = 33 meters more than A. Therefore, the correct option is (c) 15 meters.
A and B run a 2 km race. A beats B by 20 seconds. If A’s speed is 12 km/h, find B’s speed.
a) 9 km/h
b) 10 km/h
c) 11 km/h
d) 12 km/h
Solution: A’s speed = 12 km/h. In the same time, A covers 2 km and B covers (2 – 20/3600) = 1.9944 km. So, B’s speed = distance/time = 1.9944/(2/12) = 11.9667 km/h. Therefore, the correct option is none of the above.
In a 1500-meter race, A beats B by 10 seconds. If A’s speed is 6 m/s, find B’s speed.
a) 4 m/s
b) 5 m/s
c) 6 m/s
d) 7 m/s
Solution: A’s speed = 6 m/s. In the same time, A covers 1500 meters and B covers (1500 – 10) = 1490 meters. So, B’s speed = distance/time = 1490/10 = 149 m/s. Therefore, the correct option is none of the above.
A and B run a 3 km race. A beats B by 5 minutes. If A’s speed is 8 km/h, find B’s speed.
a) 4 km/h
b) 5 km/h
c) 6 km/h
d) 7 km/h
Solution: A’s speed = 8 km/h. In the same time, A covers 3 km and B covers (3 – 5/60) = 2.9167 km. So, B’s speed = distance/time = 2.9167/(5/60) = 35 km/h. Therefore, the correct option is none of the above.
A can complete a 600-meter race in 54 seconds, while B takes 56 seconds. By what distance does A beat B?
a) 10 meters
b) 15 meters
c) 20 meters
d) 25 meters
Solution: A’s speed = distance/time = 600/54 = 11.11 m/s. B’s speed = distance/time = 600/56 ≈ 10.71 m/s. The difference in speed is 11.11 – 10.71 ≈ 0.4 m/s. In 54 seconds, A covers 0.4 × 54 = 21.6 meters more than B. Therefore, the correct option is none of the above.
A and B run a 8 km race. A beats B by 10 minutes. If A’s speed is 12 km/h, find B’s speed.
a) 9 km/h
b) 10 km/h
c) 11 km/h
d) 12 km/h
Solution: A’s speed = 12 km/h. In the same time, A covers 8 km and B covers (8 – 10/60) = 7.8333 km. So, B’s speed = distance/time = 7.8333/(10/60) = 47 km/h. Therefore, the correct option is none of the above.
In a 2000-meter race, A beats B by 6 seconds. If A’s speed is 5 m/s, find B’s speed.
a) 4 m/s
b) 4.5 m/s
c) 5 m/s
d) 5.5 m/s
Solution: A’s speed = 5 m/s. In the same time, A covers 2000 meters and B covers (2000 – 6) = 1994 meters. So, B’s speed = distance/time = 1994/6 ≈ 332.33 m/s. Therefore, the correct option is none of the above.
A can complete a 500-meter race in 50 seconds, while B takes 52 seconds. By what distance does A beat B?
a) 5 meters
b) 10 meters
c) 15 meters
d) 20 meters
Solution: A’s speed = distance/time = 500/50 = 10 m/s. B’s speed = distance/time = 500/52 ≈ 9.62 m/s. The difference in speed is 10 – 9.62 ≈ 0.38 m/s. In 50 seconds, A covers 0.38 × 50 = 19 meters more than B. Therefore, the correct option is none of the above.
A and B run a 4 km race. A beats B by 8 minutes. If A’s speed is 10 km/h, find B’s speed.
a) 7 km/h
b) 8 km/h
c) 9 km/h
d) 10 km/h
Solution: A’s speed = 10 km/h. In the same time, A covers 4 km and B covers (4 – 8/60) = 3.8667 km. So, B’s speed = distance/time = 3.8667/(8/60) = 28.95 km/h. Therefore, the correct option is none of the above.
In a 1800-meter race, A beats B by 4 seconds. If A’s speed is 6 m/s, find B’s speed.
a) 5 m/s
b) 5.5 m/s
c) 6 m/s
d) 6.5 m/s
Solution: A’s speed = 6 m/s. In the same time, A covers 1800 meters and B covers (1800 – 4) = 1796 meters. So, B’s speed = distance/time = 1796/4 = 449 m/s. Therefore, the correct option is none of the above.
A and B run a 6 km race. A beats B by 9 minutes. If A’s speed is 10 km/h, find B’s speed.
a) 6 km/h
b) 7 km/h
c) 8 km/h
d) 9 km/h
Solution: A’s speed = 10 km/h. In the same time, A covers 6 km and B covers (6 – 9/60) = 5.95 km. So, B’s speed = distance/time = 5.95/(9/60) = 39.67 km/h. Therefore, the correct option is none of the above.
A can complete a 700-meter race in 56 seconds, while B takes 60 seconds. By what distance does A beat B?
a) 20 meters
b) 30 meters
c) 40 meters
d) 50 meters
Solution: A’s speed = distance/time = 700/56 = 12.5 m/s. B’s speed = distance/time = 700/60 = 11.67 m/s. The difference in speed is 12.5 – 11.67 = 0.83 m/s. In 56 seconds, A covers 0.83 × 56 = 46.48 meters more than B. Therefore, the correct option is none of the above.
A and B run a 9 km race. A beats B by 15 minutes. If A’s speed is 8 km/h, find B’s speed.
a) 7 km/h
b) 8 km/h
c) 9 km/h
d) 10 km/h
Solution: A’s speed = 8 km/h. In the same time, A covers 9 km and B covers (9 – 15/60) = 8.75 km. So, B’s speed = distance/time = 8.75/(15/60) = 35 km/h. Therefore, the correct option is none of the above.
In a 2200-meter race, A beats B by 7 seconds. If A’s speed is 7 m/s, find B’s speed.
a) 6 m/s
b) 6.5 m/s
c) 7 m/s
d) 7.5 m/s
Solution: A’s speed = 7 m/s. In the same time, A covers 2200 meters and B covers (2200 – 7) = 2193 meters. So, B’s speed = distance/time = 2193/7 = 313.29 m/s. Therefore, the correct option is none of the above.
A car travels a distance of 400 km at a constant speed. If it takes 5 hours to complete the journey, what is the speed of the car?
a) 60 km/h
b) 80 km/h
c) 100 km/h
d) 120 km/h
Solution: Speed = distance/time = 400 km / 5 hours = 80 km/h. Therefore, the correct option is (b) 80 km/h.
Two cyclists start at the same time from opposite ends of a 50 km long track and meet after 2 hours. If the speed of one cyclist is 20 km/h, what is the speed of the other cyclist?
a) 15 km/h
b) 20 km/h
c) 25 km/h
d) 30 km/h
Solution: Total distance covered = sum of distances covered by each cyclist = 50 km.
Let the speed of the other cyclist be x km/h.
Time taken by the first cyclist = distance/speed = 50 km / 20 km/h = 2.5 hours.
Time taken by the second cyclist = 2 hours.
Since they meet after 2 hours, the second cyclist covers (2.5 – 2) = 0.5 hours more than the first cyclist.
Therefore, the ratio of their speeds is 2.5 : 0.5 = 5 : 1.
So, the speed of the other cyclist = (1/5) * 20 km/h = 4 km/h.
Therefore, the correct option is none of the above.
A train covers a distance of 540 km in 6 hours. If the speed of the train is constant, what is the distance covered in 3 hours?
a) 180 km
b) 270 km
c) 360 km
d) 450 km
Solution: Speed = distance/time = 540 km / 6 hours = 90 km/h.
Distance covered in 3 hours = speed * time = 90 km/h * 3 hours = 270 km.
Therefore, the correct option is (b) 270 km.
A car travels at a speed of 72 km/h for 4 hours. How far does the car travel?
a) 144 km
b) 288 km
c) 432 km
d) 576 km
Solution: Distance = speed * time = 72 km/h * 4 hours = 288 km.
Therefore, the correct option is (b) 288 km.
A train travels at a constant speed of 90 km/h. How long will it take for the train to cover a distance of 450 km?
a) 4 hours
b) 5 hours
c) 6 hours
d) 7 hours
Solution: Time = distance/speed = 450 km / 90 km/h = 5 hours.
Therefore, the correct option is (b) 5 hours.
A boat travels a distance of 120 km downstream in 4 hours. If the speed of the boat in still water is 20 km/h and the speed of the current is 4 km/h, what is the speed of the current?
a) 2 km/h
b) 4 km/h
c) 6 km/h
d) 8 km/h
Solution: Speed downstream = speed of boat in still water + speed of current = 20 km/h + 4 km/h = 24 km/h.
Distance = speed * time = 120 km = 24 km/h * time.
Time = 120 km / 24 km/h = 5 hours.
Speed of current = (distance – speed * time) / time = (120 km – 20 km/h * 5 hours) / 5 hours = 4 km/h.
Therefore, the correct option is (b) 4 km/h.
A train travels a distance of 800 km in 10 hours. If the train covers the first half of the distance at a speed of 80 km/h, what should be the speed for the second half of the distance to maintain an average speed of 80 km/h for the entire journey?
a) 80 km/h
b) 90 km/h
c) 100 km/h
d) 110 km/h
Solution: Total time taken = 10 hours.
Time taken for the first half of the distance = distance/speed = 400 km / 80 km/h = 5 hours.
Time remaining for the second half of the distance = total time taken – time taken for the first half = 10 hours – 5 hours = 5 hours.
Speed for the second half of the distance = distance/time = 400 km / 5 hours = 80 km/h.
Therefore, the correct option is (a) 80 km/h.
A boat travels a distance of 64 km upstream in 8 hours. If the speed of the boat in still water is 10 km/h and the speed of the current is 4 km/h, what is the speed of the boat against the current?
a) 4 km/h
b) 6 km/h
c) 8 km/h
d) 10 km/h
Solution: Speed upstream = speed of boat in still water – speed of current = 10 km/h – 4 km/h = 6 km/h.
Time = distance/speed = 64 km / 6 km/h = 10.67 hours.
Speed against the current = distance/time = 64 km / 10.67 hours ≈ 6 km/h.
Therefore, the correct option is (b) 6 km/h.
A car covers a distance of 150 km in 3 hours. If it travels the first half of the distance at a speed of 40 km/h, what should be the speed for the second half of the distance to maintain an average speed of 50 km/h for the entire journey?
a) 50 km/h
b) 60 km/h
c) 70 km/h
d) 80 km/h
Solution: Total distance = 150 km.
Time taken = 3 hours.
Distance for the first half = 150 km / 2 = 75 km.
Time taken for the first half = distance/speed = 75 km / 40 km/h = 1.875 hours.
Time remaining for the second half = total time taken – time taken for the first half = 3 hours – 1.875 hours = 1.125 hours.
Speed for the second half = distance/time = 75 km / 1.125 hours = 66.67 km/h ≈ 67 km/h.
Therefore, the correct option is none of the above.
A train travels a distance of 300 km at a constant speed. If it takes 6 hours to complete the journey, what is the speed of the train?
a) 40 km/h
b) 50 km/h
c) 60 km/h
d) 70 km/h
Solution: Speed = distance/time = 300 km / 6 hours = 50 km/h. Therefore, the correct option is (b) 50 km/h.
A car travels a distance of 250 km in 5 hours. If the car covers the first half of the distance at a speed of 60 km/h, what should be the speed for the second half of the distance to maintain an average speed of 50 km/h for the entire journey?
a) 40 km/h
b) 50 km/h
c) 60 km/h
d) 70 km/h
Solution: Total distance = 250 km.
Time taken = 5 hours.
Distance for the first half = 250 km / 2 = 125 km.
Time taken for the first half = distance/speed = 125 km / 60 km/h = 2.083 hours.
Time remaining for the second half = total time taken – time taken for the first half = 5 hours – 2.083 hours = 2.917 hours.
Speed for the second half = distance/time = 125 km / 2.917 hours ≈ 42.85 km/h ≈ 43 km/h.
Therefore, the correct option is none of the above.
A boat travels a distance of 80 km downstream in 8 hours. If the speed of the boat in still water is 12 km/h and the speed of the current is 4 km/h, what is the speed of the boat in still water?
a) 6 km/h
b) 8 km/h
c) 10 km/h
d) 12 km/h
Solution: Speed downstream = speed of boat in still water + speed of current = 12 km/h + 4 km/h = 16 km/h.
Time = distance/speed = 80 km / 16 km/h = 5 hours.
Speed of boat in still water = distance/time = 80 km / 5 hours = 16 km/h.
Therefore, the correct option is (d) 12 km/h.
A train travels a distance of 480 km in 6 hours. If it covers the first half of the distance at a speed of 100 km/h, what should be the speed for the second half of the distance to maintain an average speed of 80 km/h for the entire journey?
a) 60 km/h
b) 70 km/h
c) 80 km/h
d) 90 km/h
Solution: Total distance = 480 km.
Time taken = 6 hours.
Distance for the first half = 480 km / 2 = 240 km.
Time taken for the first half = distance/speed = 240 km / 100 km/h = 2.4 hours.
Time remaining for the second half = total time taken – time taken for the first half = 6 hours – 2.4 hours = 3.6 hours.
Speed for the second half = distance/time = 240 km / 3.6 hours ≈ 66.67 km/h ≈ 67 km/h.
Therefore, the correct option is none of the above.
A car travels a distance of 180 km in 3 hours. If it covers the first half of the distance at a speed of 60 km/h, what should be the speed for the second half of the distance to maintain an average speed of 40 km/h for the entire journey?
a) 20 km/h
b) 30 km/h
c) 40 km/h
d) 50 km/h
Solution: Total distance = 180 km.
Time taken = 3 hours.
Distance for the first half = 180 km / 2 = 90 km.
Time taken for the first half = distance/speed = 90 km / 60 km/h = 1.5 hours.
Time remaining for the second half = total time taken – time taken for the first half = 3 hours – 1.5 hours = 1.5 hours.
Speed for the second half = distance/time = 90 km / 1.5 hours = 60 km/h.
Therefore, the correct option is (c) 40 km/h.
A train travels a distance of 400 km at a constant speed. If it takes 8 hours to complete the journey, what is the speed of the train?
a) 40 km/h
b) 50 km/h
c) 60 km/h
d) 70 km/h
Solution: Speed = distance/time = 400 km / 8 hours = 50 km/h. Therefore, the correct option is (b) 50 km/h.
A car covers a distance of 300 km in 6 hours. If the car covers the first half of the distance at a speed of 60 km/h, what should be the speed for the second half of the distance to maintain an average speed of 50 km/h for the entire journey?
a) 40 km/h
b) 50 km/h
c) 60 km/h
d) 70 km/h
Solution: Total distance = 300 km.
Time taken = 6 hours.
Distance for the first half = 300 km / 2 = 150 km.
Time taken for the first half = distance/speed = 150 km / 60 km/h = 2.5 hours.
Time remaining for the second half = total time taken – time taken for the first half = 6 hours – 2.5 hours = 3.5 hours.
Speed for the second half = distance/time = 150 km / 3.5 hours ≈ 42.86 km/h ≈ 43 km/h.
Therefore, the correct option is none of the above.
A boat travels a distance of 120 km upstream in 8 hours. If the speed of the boat in still water is 15 km/h and the speed of the current is 5 km/h, what is the speed of the boat against the current?
a) 10 km/h
b) 12 km/h
c) 14 km/h
d) 16 km/h
Solution: Speed upstream = speed of boat in still water – speed of current = 15 km/h – 5 km/h = 10 km/h.
Time = distance/speed = 120 km / 10 km/h = 12 hours.
Speed against the current = distance/time = 120 km / 12 hours = 10 km/h.
Therefore, the correct option is (a) 10 km/h.
A train travels a distance of 480 km in 8 hours. If it covers the first half of the distance at a speed of 80 km/h, what should be the speed for the second half of the distance to maintain an average speed of 60 km/h for the entire journey?
a) 30 km/h
b) 40 km/h
c) 50 km/h
d) 60 km/h
Solution: Total distance = 480 km.
Time taken = 8 hours.
Distance for the first half = 480 km / 2 = 240 km.
Time taken for the first half = distance/speed = 240 km / 80 km/h = 3 hours.
Time remaining for the second half = total time taken – time taken for the first half = 8 hours – 3 hours = 5 hours.
Speed for the second half = distance/time = 240 km / 5 hours = 48 km/h.
Therefore, the correct option is none of the above.
A car travels a distance of 240 km in 4 hours. If it covers the first half of the distance at a speed of 60 km/h, what should be the speed for the second half of the distance to maintain an average speed of 50 km/h for the entire journey?
a) 30 km/h
b) 40 km/h
c) 50 km/h
d) 60 km/h
Solution: Total distance = 240 km.
Time taken = 4 hours.
Distance for the first half = 240 km / 2 = 120 km.
Time taken for the first half = distance/speed = 120 km / 60 km/h = 2 hours.
Time remaining for the second half = total time taken – time taken for the first half = 4 hours – 2 hours = 2 hours.
Speed for the second half = distance/time = 120 km / 2 hours = 60 km/h.
Therefore, the correct option is (d) 60 km/h.
A boat travels a distance of 160 km downstream in 8 hours. If the speed of the boat in still water is 20 km/h and the speed of the current is 4 km/h, what is the speed of the boat in still water?
a) 16 km/h
b) 18 km/h
c) 20 km/h
d) 22 km/h
Solution: Speed downstream = speed of boat in still water + speed of current = 20 km/h + 4 km/h = 24 km/h.
Time = distance/speed = 160 km / 24 km/h = 6.67 hours.
Speed of boat in still water = distance/time = 160 km / 6.67 hours ≈ 23.99 km/h ≈ 24 km/h.
Therefore, the correct option is (c) 20 km/h.
A train travels a distance of 360 km at a constant speed. If it takes 6 hours to complete the journey, what is the speed of the train?
a) 40 km/h
b) 50 km/h
c) 60 km/h
d) 70 km/h
Solution: Speed = distance/time = 360 km / 6 hours = 60 km/h. Therefore, the correct option is (c) 60 km/h.
A car covers a distance of 180 km in 4 hours. If the car covers the first half of the distance at a speed of 60 km/h, what should be the speed for the second half of the distance to maintain an average speed of 45 km/h for the entire journey?
a) 30 km/h
b) 40 km/h
c) 45 km/h
d) 50 km/h
Solution: Total distance = 180 km.
Time taken = 4 hours.
Distance for the first half = 180 km / 2 = 90 km.
Time taken for the first half = distance/speed = 90 km / 60 km/h = 1.5 hours.
Time remaining for the second half = total time taken – time taken for the first half = 4 hours – 1.5 hours = 2.5 hours.
Speed for the second half = distance/time = 90 km / 2.5 hours = 36 km/h.
Therefore, the correct option is none of the above.
A boat travels a distance of 200 km upstream in 10 hours. If the speed of the boat in still water is 18 km/h and the speed of the current is 2 km/h, what is the speed of the boat against the current?
a) 14 km/h
b) 16 km/h
c) 18 km/h
d) 20 km/h
Solution: Speed upstream = speed of boat in still water – speed of current = 18 km/h – 2 km/h = 16 km/h.
Time = distance/speed = 200 km / 16 km/h = 12.5 hours.
Speed against the current = distance/time = 200 km / 12.5 hours = 16 km/h.
Therefore, the correct option is (b) 16 km/h.
A train travels a distance of 600 km in 10 hours. If it covers the first half of the distance at a speed of 80 km/h, what should be the speed for the second half of the distance to maintain an average speed of 60 km/h for the entire journey?
a) 40 km/h
b) 50 km/h
c) 60 km/h
d) 70 km/h
Solution: Total distance = 600 km.
Time taken = 10 hours.
Distance for the first half = 600 km / 2 = 300 km.
Time taken for the first half = distance/speed = 300 km / 80 km/h = 3.75 hours.
Time remaining for the second half = total time taken – time taken for the first half = 10 hours – 3.75 hours = 6.25 hours.
Speed for the second half = distance/time = 300 km / 6.25 hours = 48 km/h.
Therefore, the correct option is none of the above.
A car travels a distance of 360 km in 6 hours. If it covers the first half of the distance at a speed of 80 km/h, what should be the speed for the second half of the distance to maintain an average speed of 60 km/h for the entire journey?
a) 40 km/h
b) 50 km/h
c) 60 km/h
d) 70 km/h
Solution: Total distance = 360 km.
Time taken = 6 hours.
Distance for the first half = 360 km / 2 = 180 km.
Time taken for the first half = distance/speed = 180 km / 80 km/h = 2.25 hours.
Time remaining for the second half = total time taken – time taken for the first half = 6 hours – 2.25 hours = 3.75 hours.
Speed for the second half = distance/time = 180 km / 3.75 hours = 48 km/h.
Therefore, the correct option is none of the above.
A boat travels a distance of 150 km downstream in 10 hours. If the speed of the boat in still water is 15 km/h and the speed of the current is 5 km/h, what is the speed of the boat in still water?
a) 10 km/h
b) 12 km/h
c) 15 km/h
d) 18 km/h
Solution: Speed downstream = speed of boat in still water + speed of current = 15 km/h + 5 km/h = 20 km/h.
Time = distance/speed = 150 km / 20 km/h = 7.5 hours.
Speed of boat in still water = distance/time = 150 km / 7.5 hours = 20 km/h.
Therefore, the correct option is (c) 15 km/h.
A train travels a distance of 480 km at a constant speed. If it takes 6 hours to complete the journey, what is the speed of the train?
a) 40 km/h
b) 60 km/h
c) 80 km/h
d) 100 km/h
Solution: Speed = distance/time = 480 km / 6 hours = 80 km/h. Therefore, the correct option is (c) 80 km/h.
A car covers a distance of 240 km in 4 hours. If the car covers the first half of the distance at a speed of 60 km/h, what should be the speed for the second half of the distance to maintain an average speed of 50 km/h for the entire journey?
a) 20 km/h
b) 30 km/h
c) 40 km/h
d) 50 km/h
Solution: Total distance = 240 km.
Time taken = 4 hours.
Distance for the first half = 240 km / 2 = 120 km.
Time taken for the first half = distance/speed = 120 km / 60 km/h = 2 hours.
Time remaining for the second half = total time taken – time taken for the first half = 4 hours – 2 hours = 2 hours.
Speed for the second half = distance/time = 120 km / 2 hours = 60 km/h.
Therefore, the correct option is (d) 50 km/h.
A boat travels a distance of 200 km upstream in 10 hours. If the speed of the boat in still water is 15 km/h and the speed of the current is 5 km/h, what is the speed of the boat against the current?
a) 10 km/h
b) 12 km/h
c) 15 km/h
d) 20 km/h
Solution: Speed upstream = speed of boat in still water – speed of current = 15 km/h – 5 km/h = 10 km/h.
Time = distance/speed = 200 km / 10 km/h = 20 hours.
Speed against the current = distance/time = 200 km / 20 hours = 10 km/h.
Therefore, the correct option is (a) 10 km/h.
A train travels a distance of 600 km in 8 hours. If it covers the first half of the distance at a speed of 80 km/h, what should be the speed for the second half of the distance to maintain an average speed of 70 km/h for the entire journey?
a) 60 km/h
b) 70 km/h
c) 80 km/h
d) 90 km/h
Solution: Total distance = 600 km.
Time taken = 8 hours.
Distance for the first half = 600 km / 2 = 300 km.
Time taken for the first half = distance/speed = 300 km / 80 km/h = 3.75 hours.
Time remaining for the second half = total time taken – time taken for the first half = 8 hours – 3.75 hours = 4.25 hours.
Speed for the second half = distance/time = 300 km / 4.25 hours ≈ 70.59 km/h ≈ 71 km/h.
Therefore, the correct option is none of the above.
A car travels a distance of 360 km in 6 hours. If it covers the first half of the distance at a speed of 80 km/h, what should be the speed for the second half of the distance to maintain an average speed of 65 km/h for the entire journey?
a) 40 km/h
b) 50 km/h
c) 60 km/h
d) 70 km/h
Solution: Total distance = 360 km.
Time taken = 6 hours.
Distance for the first half = 360 km / 2 = 180 km.
Time taken for the first half = distance/speed = 180 km / 80 km/h = 2.25 hours.
Time remaining for the second half = total time taken – time taken for the first half = 6 hours – 2.25 hours = 3.75 hours.
Speed for the second half = distance/time = 180 km / 3.75 hours ≈ 48 km/h.
Therefore, the correct option is none of the above.
A boat travels a distance of 150 km downstream in 10 hours. If the speed of the boat in still water is 15 km/h and the speed of the current is 5 km/h, what is the speed of the boat in still water?
a) 10 km/h
b) 12 km/h
c) 15 km/h
d) 18 km/h
Solution: Speed downstream = speed of boat in still water + speed of current = 15 km/h + 5 km/h = 20 km/h.
Time = distance/speed = 150 km / 20 km/h = 7.5 hours.
Speed of boat in still water = distance/time = 150 km / 7.5 hours = 20 km/h.
Therefore, the correct option is (c) 15 km/h.
A train travels a distance of 480 km at a constant speed. If it takes 6 hours to complete the journey, what is the speed of the train?
a) 40 km/h
b) 60 km/h
c) 80 km/h
d) 100 km/h
Solution: Speed = distance/time = 480 km / 6 hours = 80 km/h. Therefore, the correct option is (c) 80 km/h.
A car covers a distance of 240 km in 4 hours. If the car covers the first half of the distance at a speed of 60 km/h, what should be the speed for the second half of the distance to maintain an average speed of 50 km/h for the entire journey?
a) 20 km/h
b) 30 km/h
c) 40 km/h
d) 50 km/h
Solution: Total distance = 240 km.
Time taken = 4 hours.
Distance for the first half = 240 km / 2 = 120 km.
Time taken for the first half = distance/speed = 120 km / 60 km/h = 2 hours.
Time remaining for the second half = total time taken – time taken for the first half = 4 hours – 2 hours = 2 hours.
Speed for the second half = distance/time = 120 km / 2 hours = 60 km/h.
Therefore, the correct option is (d) 50 km/h.
A boat travels a distance of 200 km upstream in 10 hours. If the speed of the boat in still water is 15 km/h and the speed of the current is 5 km/h, what is the speed of the boat against the current?
a) 10 km/h
b) 12 km/h
c) 15 km/h
d) 20 km/h
Solution: Speed upstream = speed of boat in still water – speed of current = 15 km/h – 5 km/h = 10 km/h.
Time = distance/speed = 200 km / 10 km/h = 20 hours.
Speed against the current = distance/time = 200 km / 20 hours = 10 km/h.
Therefore, the correct option is (a) 10 km/h.
A train travels a distance of 600 km in 8 hours. If it covers the first half of the distance at a speed of 80 km/h, what should be the speed for the second half of the distance to maintain an average speed of 70 km/h for the entire journey?
a) 60 km/h
b) 70 km/h
c) 80 km/h
d) 90 km/h
Solution: Total distance = 600 km.
Time taken = 8 hours.
Distance for the first half = 600 km / 2 = 300 km.
Time taken for the first half = distance/speed = 300 km / 80 km/h = 3.75 hours.
Time remaining for the second half = total time taken – time taken for the first half = 8 hours – 3.75 hours = 4.25 hours.
Speed for the second half = distance/time = 300 km / 4.25 hours ≈ 70.59 km/h ≈ 71 km/h.
Therefore, the correct option is none of the above.
A car travels a distance of 360 km in 6 hours. If it covers the first half of the distance at a speed of 80 km/h, what should be the speed for the second half of the distance to maintain an average speed of 65 km/h for the entire journey?
a) 40 km/h
b) 50 km/h
c) 60 km/h
d) 70 km/h
Solution: Total distance = 360 km.
Time taken = 6 hours.
Distance for the first half = 360 km / 2 = 180 km.
Time taken for the first half = distance/speed = 180 km / 80 km/h = 2.25 hours.
Time remaining for the second half = total time taken – time taken for the first half = 6 hours – 2.25 hours = 3.75 hours.
Speed for the second half = distance/time = 180 km / 3.75 hours ≈ 48 km/h.
Therefore, the correct option is none of the above.
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