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Race Winner

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Director
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Status: Preparing for the 4th time -:(
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Race Winner [#permalink] New post 10 Nov 2011, 15:39
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Question Stats:

41% (02:47) correct 58% (01:08) wrong based on 17 sessions
Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?

I. Stephanie II. Regine III. Brian
I only
II only
III only
I or II only
I, II, or III

Can someone please tell the approach how to solve this problem?
[Reveal] Spoiler: OA

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Re: Race Winner [#permalink] New post 10 Nov 2011, 20:51
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Let S, R, and B be the times that it took Stephanie, Regine, and Brian to run a 20 mile race.

From the problem: S + R = B + 2

The fastest speed was 8mph, which means the the lowest time was 20/8 = 2.5 hours, meaning that anyone who ran slower than 8mph would have finished in more than 2.5 hours.

From the equation above, you can see that B is lowest when S and R are as small as possible, and the minimum value for S and R is 2.5. So:

2.5 + 2.5 = B + 2
B = 3

The fastest (lowest) possible time for B is 3 hours, which is still slower than 2.5 hours for S and R. Therefore, either S or R could have won, but not B.
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Re: Race Winner [#permalink] New post 19 Nov 2011, 00:35
Agree with GMATmission.
The basis of assumption can be questioned in the explanation.
So,in my opinion,the winner can be anyone among I, II, III.
Director
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Re: Race Winner [#permalink] New post 19 Nov 2011, 13:10
kostyan5 wrote:
Let S, R, and B be the times that it took Stephanie, Regine, and Brian to run a 20 mile race.

From the problem: S + R = B + 2

The fastest speed was 8mph, which means the the lowest time was 20/8 = 2.5 hours, meaning that anyone who ran slower than 8mph would have finished in more than 2.5 hours.

From the equation above, you can see that B is lowest when S and R are as small as possible, and the minimum value for S and R is 2.5. So:

2.5 + 2.5 = B + 2
B = 3

The fastest (lowest) possible time for B is 3 hours, which is still slower than 2.5 hours for S and R. Therefore, either S or R could have won, but not B.




Hi kostyan5,

Can you please clarify how you have assumed S and R to be 2.5 because even B can also be 2.5 right?
if in that case anyone i.e S or R or B can win the race,please clarify on the same
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Re: Race Winner [#permalink] New post 23 Nov 2011, 10:35
I think the answer is E as we do not exactly know who is slower than the other two.
Re: Race Winner   [#permalink] 23 Nov 2011, 10:35
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