1️⃣ A runner covers 100 meters in 10 seconds. What is the runner's speed in meters per second (m/s)?
Step-by-Step Explanation
Speed = Distance / Time
Speed = 100 meters / 10 seconds
Speed = 10 m/s
Answer: 10 m/s ✅
2️⃣ A car travels at a speed of 60 km/h. How much distance will it cover in 2 hours?
Step-by-Step Explanation
Distance = Speed * Time
Distance = 60 km/h * 2 hours
Distance = 120 km
Answer: 120 km ✅
3️⃣ A cyclist covers 15 km in 3 hours. What is the cyclist's speed in km/h?
Step-by-Step Explanation
Speed = Distance / Time
Speed = 15 km / 3 hours
Speed = 5 km/h
Answer: 5 km/h ✅
4️⃣ A and B run a 100-meter race. A's speed is 5 m/s, and B's speed is 4 m/s. How much start does A give to B so that they finish the race at the same time?
Step-by-Step Explanation
Time taken by A to complete the race = 100 meters / 5 m/s = 20 seconds.
Distance covered by B in 20 seconds = 4 m/s * 20 seconds = 80 meters.
Start given by A to B = 100 meters - 80 meters = 20 meters.
Answer: 20 meters ✅
5️⃣ In a 1 km race, A beats B by 100 meters. If A's speed is 10 m/s, what is B's speed?
Step-by-Step Explanation
1 km = 1000 meters.
Time taken by A to complete the race = 1000 meters / 10 m/s = 100 seconds.
Distance covered by B in 100 seconds = 1000 meters - 100 meters = 900 meters.
B's speed = 900 meters / 100 seconds = 9 m/s.
Answer: 9 m/s ✅
6️⃣ A and B run a 400-meter race. A's speed is 16 km/h, and B's speed is 10 km/h. By what distance does A beat B?
Step-by-Step Explanation
Convert speeds to m/s: A's speed = 16 * (5/18) m/s = 40/9 m/s, B's speed = 10 * (5/18) m/s = 25/9 m/s.
Time taken by A to complete the race = 400 meters / (40/9 m/s) = 90 seconds.
Distance covered by B in 90 seconds = (25/9 m/s) * 90 seconds = 250 meters.
Distance by which A beats B = 400 meters - 250 meters = 150 meters.
Answer: 150 meters ✅
7️⃣ A runs 1 3/4 times as fast as B. If A gives B a start of 84 meters, how far must the winning post be so that A and B reach it at the same time?
Step-by-Step Explanation
A's speed = 7/4 * B's speed.
Let B's speed be 'x' m/s, then A's speed is 7x/4 m/s.
Let the distance to the winning post be 'd' meters.
Time taken by A = d / (7x/4) = 4d / 7x.
Time taken by B = (d - 84) / x.
4d / 7x = (d - 84) / x
4d / 7 = d - 84
4d = 7d - 588
3d = 588
d = 196 meters.
This is the distance B runs.
Total distance = d + 84 = 196 + 84 = 280 meters.
Answer: 280 meters ✅
8️⃣ In a 1000-meter race, A beats B by 100 meters or 10 seconds. What is A's speed?
Step-by-Step Explanation
B runs 100 meters in 10 seconds, so B's speed = 100 meters / 10 seconds = 10 m/s.
Time taken by B to run 1000 meters = 1000 meters / 10 m/s = 100 seconds.
A beats B by 10 seconds, so A takes 100 - 10 = 90 seconds.
9️⃣ A, B, and C run a race of 1000 meters. A beats B by 100 meters and C by 150 meters. If B and C run a race of 1000 meters, by what distance will B beat C?
Step-by-Step Explanation
When A runs 1000 meters, B runs 900 meters and C runs 850 meters.
Ratio of B's speed to C's speed = 900 : 850 = 18 : 17.
When B runs 1000 meters, C runs (17/18) * 1000 = 17000/18 = 8500/9 meters.
Distance by which B beats C = 1000 - 8500/9 = (9000 - 8500)/9 = 500/9 = 55.55 meters.