In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?
Answer: C
Let the speed of the slowest runner be s m/min and the speed of the fastest runner be 2s m/min.
Length of the race track = 1000 m and the two runners meet after 5 minutes.
∴ Relative speed = 1000/5 = 200 m/min
∴ 2s − s = 200
∴ s = 200 m/min
∴ The speed of the fastest runner = 2s = 400 m/min
∴ The time taken by the fastest runner to complete the race = 4000/400 = 10 min
Hence, option (c).
Alternatively,
The slowest runner covers 500 m when the fastest runner covers 1000 m.
∴ The two meet at the starting point when the fastest runner covers 2000 m and the slowest runner covers 1000 m.
∴ The fastest runner runs 2000 m in 5 minutes.
∴ He runs 4000 m in 10 minutes.
Hence, option (c).