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.