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In a 4000 meter race around a circular stadium having a circumference

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Bunuel
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In a 4000 meter race around a circular stadium having a circumference [#permalink] In a 4000 meter race around a circular stadium having a circumference   08 Jan 2020, 04:09
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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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Re: In a 4000 meter race around a circular stadium having a circumference [#permalink] 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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Re: In a 4000 meter race around a circular stadium having a circumference [#permalink] In a 4000 meter race around a circular stadium having a circumference   09 Jan 2020, 04:18
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Bunuel wrote:
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

Are You Up For the Challenge: 700 Level Questions


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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Re: In a 4000 meter race around a circular stadium having a circumference [#permalink] In a 4000 meter race around a circular stadium having a circumference   10 Jan 2020, 17:32
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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Re: In a 4000 meter race around a circular stadium having a circumference [#permalink] In a 4000 meter race around a circular stadium having a circumference   10 Jan 2020, 22:42
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Bunuel wrote:
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

Are You Up For the Challenge: 700 Level Questions



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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Re: In a 4000 meter race around a circular stadium having a circumference [#permalink] In a 4000 meter race around a circular stadium having a circumference   10 Jan 2020, 23:17
Bunuel wrote:
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


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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Re: In a 4000 meter race around a circular stadium having a circumference [#permalink] In a 4000 meter race around a circular stadium having a circumference   03 May 2024, 11:58
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Re: In a 4000 meter race around a circular stadium having a circumference [#permalink]
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