blowice27 wrote:
n 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.
A. 36 minute
B. 24 minute
C. 16 minute
D. 12 minute
E. 10 minute
Given:
1. 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.
2. All the runners maintain uniform speed throughout the race.
Asked: 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.
Let the speed of the slowest and the fastest runner be x and 3x m/s respectively
In the race there are 9 laps of 400 m each totalling 3600m .
Relative speed = 3x - x = 2x m/s
Distance = time * speed
400 = 4*60 2x
x = 10/12= 5/6 m/s
Speed of the slowest runner = x = = 5/6 m/s
Speed of the fastest runner = 3x = 5/2 = 2.5 m/s
Time taken by the fastest runner to finish the race = 3600/2.5 = 1440 seconds = 24 mins
IMO B
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