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Two horses begin running on an oval course at the same time.

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Two horses begin running on an oval course at the same time. [#permalink] New post 29 Apr 2012, 21:23
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67% (02:09) correct 33% (01:30) wrong based on 103 sessions
Two horses begin running on an oval course at the same time. One runs each lap in 9 minutes; the other takes 12 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?

A. 36
B. 12
C. 9
D. 4
E. 3
[Reveal] Spoiler: OA
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Re: Word Problem [#permalink] New post 29 Apr 2012, 22:12
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The best approach in my view is like this:
Check from the answer options.
As one horse completes the lap in 9 minutes and the other in 12 minutes, the answer is definitely greater than 12, because by 12 minutes, faster on completes 12/9 = 1.33 laps and the slower one completes only 1 lap, which results in a gap of 1.33 - 1 = 0.33 laps, which is less than 1 lap.
The only option looks feasible is option-A, ie., 36 min.
With out checking we can go for that. But let us check:
After 36 min, faster one completes 36/9 = 4 laps and
slower one completes 36/12 = 3 laps.
The faster one covered exactly one more lap than the slower one did.
Answer 'A'
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Re: Word Problem [#permalink] New post 29 Apr 2012, 22:31
Thank you for the clarification Ravi. Your method makes sense to me.
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Re: Two horses begin running on an oval course at the same time. [#permalink] New post 29 Apr 2012, 22:51
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rakp wrote:
Two horses begin running on an oval course at the same time. One runs each lap in 9 minutes; the other takes 12 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?

A. 36
B. 12
C. 9
D. 4
E. 3


The rate of the faster horse is 1/9 lap/minute;
The rate of the slower horse is 1/12 lap/minute;

Their relative rate is 1/9-1/12=1/36 lap/minute;

The faster horse to gain one full lap will need time=distance/rate=1/(1/36)=36 minutes.

Answer: A.

Hope it's clear.
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Re: Two horses begin running on an oval course at the same time. [#permalink] New post 14 Nov 2013, 08:50
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Re: Two horses begin running on an oval course at the same time. [#permalink] New post 14 Nov 2013, 17:19
The easiest way is to check with answers

A) 36 min i.e horse A 4 laps and horse B 3 laps
Hence A
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Re: Two horses begin running on an oval course at the same time. [#permalink] New post 16 Nov 2013, 05:29
Isn't the LCM of the two numbers the solution since the question is asking for mins?
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Re: Two horses begin running on an oval course at the same time.   [#permalink] 16 Nov 2013, 05:29
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Two horses begin running on an oval course at the same time.

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