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In a one-kilometre race, A beats B by 15 seconds and B beats C by 15 seconds. If C is 100 metres away from the finishing mark, when B has reached it, find the speed of A.
1. 25/3 m/sec
2. 24/5 m/sec
3. 25/6 m/sec
4. 25/7 m/sec

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Best answer
Correct Answer - Option 1 : 25/3 m/sec

Given

Total distance = 1 Km

Speed method 

Let B take x seconds to run 1000 m.

∴ Time taken by C = (x + 15) seconds

Calculation

∴ \(\frac{{x}}{{x\;+\;15}}= \frac{{900}}{{1000}}= \frac{{9}}{{10}}\)

⇒ 10x = 9x + 135

⇒ x = 135 seconds

Now in a one-kilometer race, A beats B by 15 seconds. 

It means A covers 1000 m in 135 - 15 = 120 seconds

∴ Speed of \(A = \frac{{1000}}{{120}} = \frac{{25}}{3}m/\sec \)

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