##### In a 1600 m race around a circular track of length 400 m, the faster r...

In a 1600 m race around a circular track of length 400 m, the faster runner and the slowest runner meet at the end of the sixth minute, for the first time after the start of the race. All the runners maintain uniform speed throughout the race. If the faster runner runs at twice the speed of the slowest runner. Find the time taken by the faster runner to finish the race.

A) 3 minutes

B) 6 minutes

C) 12 minutes

D) 24 minutes

Ans. (C)

speed of slowest runner = x m/m

speed of fastest runner = 2x m/m

fastest runner will run with a relative speed of 2x - x = x with respect to slowest runner.

They meet after 6th minute. That means this is the 2nd round of fastest runner and it's the 1st round of slowest runner.

so the relative distance covered by fastest runner in 6 minutes will be 400m with respect to slowest runner.

we know, distance = speed * time

400 = x * 6

x = 400/6.

Hence speed of fastest runner = 2 x = 400 / 3.

Hence time taken to cover 1600 metres:

time = distance / speed

time = 1600/ (400/3)

time = 12 minutes.