Question

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, then what shall be the time taken by the fastest runner to finish the said race?

• A. 15 minutes
• B. 20 minutes
• C. 10 minutes
• D. 13 minutes
• E. 5 minutes

Hint:

On a circular track, the time for two runners starting together to meet again is the lap length divided by their relative speed.

Answer 1

The Correct Option is C

Step 1: Define Speeds:
Let speed of slowest runner = $v$ m/min. Then speed of fastest runner = $2v$ m/min.
Step 2: Relative Speed and Meeting:
They start together. They meet again when the fastest has gained one full lap over the slowest. The circumference is 1000 m. Time for first meeting after start = $\frac{\text{Lap length}}{\text{Relative speed}} = \frac{1000}{2v - v} = \frac{1000}{v}$ minutes.
Step 3: Use Given Meeting Time:
This first meeting happens at the end of the 5th minute (given). So, $\frac{1000}{v} = 5 \implies v = 200$ m/min. Thus, fastest runner's speed = $2v = 400$ m/min.
Step 4: Time for Fastest to Finish Race:
Race distance = 4000 m. Time = $\frac{4000}{400} = 10$ minutes.
Step 5: Final Answer:
The fastest runner takes 10 minutes to finish the race.