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Bunuel
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In a 4000 meter race around a circular stadium having a circumference 08 Jan 2020, 04:09
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69% (02:32) correct 31% (02:38) wrong based on 287 sessions

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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?

(A) 20 min
(B) 15 min
(C) 10 min
(D) 5 min
(E) 3 min

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C
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BhishmaNaidu99
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In a 4000 meter race around a circular stadium having a circumference 08 Jan 2020, 04:41
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As the fastest runs twice the speed of slowest , the distance covered will be twice the distance covered

while slower completes one round , the fastest completes two rounds in 5 min , and they meet each other at this point

d = s * t
2000 = s * 5
s= 400 mt / min

total time = 4000/400 = 10 min
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rajatchopra1994
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In a 4000 meter race around a circular stadium having a circumference 09 Jan 2020, 04:18
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Bunuel
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?

(A) 20 min
(B) 15 min
(C) 10 min
(D) 5 min
(E) 3 min

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Relative speed = F(fastest)-S(slowest)
Relative time = 5min. = 300 seconds
Relative distance = 1000
also, F = 2S
Hence,by solving 2S - S = 1000/5 = 200 (metres/min.)

Time taken to finish race = 4000 / 400 = 10 min

IMO-C
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In a 4000 meter race around a circular stadium having a circumference 10 Jan 2020, 17:32
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I got A by using the ansers.

Why am I wrong? =/

A 4000mts/15min*60sec = 3.33 mps * 360sec (at the end of 5th minute, hence 6 minutes) = 1,600 mts travelled.

So B had a speed of 1.66 mps * 360sec = 600 mts.

So after 6 minutes B will be in the 600 mts mark and A will also be in that mark with one lap ahead.

What am I missing?

Kind regards!
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In a 4000 meter race around a circular stadium having a circumference 10 Jan 2020, 22:42
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Bunuel
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?

(A) 20 min
(B) 15 min
(C) 10 min
(D) 5 min
(E) 3 min

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We know,
circular track = 1000 mtrs.
race = 4000 mtrs.

According to the question, after 5th minute both, slow and the fast runner meet at the starting point.
Slow runner's speed= 1000/5 = 200 mtrs./min
Fast runner's speed = 200 * 2 = 400 mtrs./min

In the 5th min., fast runner has covered = 400*5 = 2000 mtrs.
In the 5th min., slow runner has covered = 200*5 = 1000 mtrs.

If it took 5 mins., to complete 2000 mtrs., it will take another 5 mins to complete 4000 mtrs.

Thus, total of 10 mins to finish the race.
The correct option is C.
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In a 4000 meter race around a circular stadium having a circumference 10 Jan 2020, 23:17
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Bunuel
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?

(A) 20 min
(B) 15 min
(C) 10 min
(D) 5 min
(E) 3 min

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ST=D
If the fastest runner runs at twice the speed of the slowest runner, then the distance covered by fast runner will also be twice the distance covered by slower runner.
When distance covered by slower runner for the first time is 1000m, so distance covered by fast runner is 2000m in 5 minutes.

So time taken by fast runner to cover 4000 m is 10 minutes

C is correct
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In a 4000 meter race around a circular stadium having a circumference 21 Oct 2025, 15:59
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The ratio of the speeds of the fastest and slowest runners is 2:1, and both are running in the same direction. This means they will have only one meeting point, since the faster runner will continuously gain on the slower one and meet him only when he has completed one full lap more.

Logically, that meeting point must be the starting point. For example, when the faster runner completes 1000 meters, the slower runner covers only 500 meters. When the faster runner reaches 2000 meters, the slower runner reaches 1000 meters, which brings both back to the starting point. Hence, the only possible meeting point is the start line.

The question tells us that this meeting happens in the 5th minute. At that time, the faster runner has completed 2 rounds, and the slower runner has completed 1 round. Since the faster runner needs to complete 4 rounds to win the race, he will take 10 minutes complete the race
Option C
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