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.
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.