Question

in a 3600 m race around a circular track of length 400m, the faster runner and the slowest runner meet at the end of the fourth 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 thrice the speed of the slowest runner. find the time taken by the faster runner to finish the race.

Answer 1

Assuming that all runners starts from the same point.

Let the speed of the fastest runner = 3x m/s

speed of the slowest runner = x m/s

Relative speed of the fastest runner with respect the slowest runner

=3x−x=2x

When the fastest and slowest runners meet for the first time, fastest runner would have run 1 round (400 m) more when compared to the slowest runner.

i.e., in 4 min (240 sec), fastest runner run 400 m more when compared to the slowest runner.

400/2x=240

5/2x=3

x=5/6

Speed of the fastest runner =3x=3×5/6=2.5 m/s

Time taken by the faster runner to finish the race

=3600/2.5=1440 seconds = 24 minutes   ANS

SECOND PROCESS

In 4 min, fastest runner run 400 m more when compared to the slowest runner.

Speed of the fastest runner : Speed of the slowest runner = 3 : 1

Suppose slowest runner runs x km in 4 min

Then the fastest runner runs 3x km in 4 min

then 2x=400

x=200

i.e., in 4 min, fastest runner run 3x=600 m

i.e., in 1 min, fastest runner run 600/4=150 m

Time taken by the fastest runner to finish the race = 3600/150

=24 min  ANS

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