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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
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In a 1600 m race around a circular track of length 400 m, the faster r...
As, the faster runner is twice as fast as the slowest runner, the faster runner would have complete two rounds by the time the slowest runner completes one round.
Their first meeting takes place after the fastest runner takes 6 min to complete two rounds and the slowest runner completes one round.
Time taken to complete one round by fastest runner = 6/2 = 3 minutes
Rounds needed to complete the race = 1600/400 = 4
Time taken to complete the race = 4 × 3 = 12 min
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Most Upvoted Answer
In a 1600 m race around a circular track of length 400 m, the faster r...
Let's assume that the slowest runner completes one lap of the circular track in T minutes. Since the track length is 400 m, the slowest runner's speed is 400/T m/min.

We are given that the faster runner runs at twice the speed of the slowest runner. So, the faster runner's speed is 2 * (400/T) m/min.

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. This means that in six minutes, the faster runner has completed one full lap more than the slowest runner.

Let's calculate the distance covered by the slowest runner in six minutes:
Distance covered by the slowest runner = Speed of the slowest runner * Time = (400/T) * 6 = 2400/T m

Now, let's calculate the distance covered by the faster runner in six minutes:
Distance covered by the faster runner = Speed of the faster runner * Time = (2 * (400/T)) * 6 = 4800/T m

Since the faster runner has completed one full lap more than the slowest runner, the distance covered by the faster runner in six minutes is equal to one lap of the circular track, which is 400 m.

Therefore, we have the equation:
4800/T = 400

Solving this equation, we get:
T = 4800/400 = 12 minutes

Hence, the time taken by the faster runner to finish the race is 12 minutes. Therefore, the correct answer is option (c).
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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 minutesb)6 minutesc)12 minutesd)24 minutesCorrect answer is option 'C'. Can you explain this answer?
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