A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:5.15 kmph4.14 kmph4.25 kmph4.4 kmphNone
Question
A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:5.15 kmph4.14 kmph4.25 kmph4.4 kmphNone
Solution 1
To solve this problem, we first need to convert the speed of A from km/h to m/s because the distance is given in meters and the time in seconds. We know that 1 km = 1000 m and 1 hour = 3600 seconds.
So, the speed of A = 5 kmph = 5 * 1000 / 3600 = 1.39 m/s.
Now, the time taken by A to cover the 100 m distance = Distance / Speed = 100 / 1.39 = 71.94 seconds.
Since A beats B by 8 seconds, the time taken by B to cover the 92 m distance (because B was given a start of 8 m) = 71.94 + 8 = 79.94 seconds.
So, the speed of B = Distance / Time = 92 / 79.94 = 1.15 m/s.
To convert this speed back to km/h, we use the conversion 1 m/s = 3.6 km/h.
So, the speed of B = 1.15 * 3.6 = 4.14 kmph.
Therefore, the speed of B is 4.14 kmph.
Solution 2
First, we need to convert the speed of A from km/hr to m/sec because the distance is given in meters and the time in seconds. We know that 1 km = 1000 m and 1 hour = 3600 seconds. So, 5 km/hr = 5 * (1000/3600) = 1.39 m/sec.
Now, the time taken by A to cover the 100 m distance is distance/speed = 100/1.39 = 71.94 seconds.
Since A beats B by 8 seconds, the time taken by B to run 100 m is 71.94 + 8 = 79.94 seconds.
But B was given a start of 8 m, so the actual distance covered by B is 100 - 8 = 92 m.
Therefore, the speed of B is distance/time = 92/79.94 = 1.15 m/sec.
To convert this speed back to km/hr, we use the conversion 1 m/sec = 3.6 km/hr. So, the speed of B is 1.15 * 3.6 = 4.14 km/hr.
So, the correct answer is 4.14 kmph.
Solution 3
To solve this problem, we first need to convert the speed of A from km/h to m/s because the distance and the start given to B are in meters.
1 km = 1000 m 1 hour = 3600 seconds
So, 5 km/h = 5 * (1000/3600) = 1.39 m/s
Now, the time taken by A to cover the 100 m distance is Distance/Speed = 100/1.39 = 71.94 seconds.
Since A beats B by 8 seconds, the time taken by B to run 100 m is 71.94 + 8 = 79.94 seconds.
But B was given a start of 8 m, so the actual distance covered by B is 100 - 8 = 92 m.
Therefore, the speed of B = Distance/Time = 92/79.94 = 1.15 m/s.
To convert this back to km/h, we use the conversion factor 3600/1000, so the speed of B = 1.15 * (3600/1000) = 4.14 km/h.
So, the correct answer is 4.14 kmph.
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