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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine'

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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine' [#permalink] New post 10 Nov 2011, 14:39
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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

A. I only
B. II only
C. III only
D. I or II only
E. I, II, or III

OPEN DISCUSSION OF THIS QUESTION IS HERE: stephanie-regine-and-brian-ran-a-20-mile-race-stephanie-127050.html
[Reveal] Spoiler: OA

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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine' [#permalink] New post 10 Nov 2011, 19:51
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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: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine' [#permalink] New post 18 Nov 2011, 23:35
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.
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine' [#permalink] New post 19 Nov 2011, 12:10
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: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine' [#permalink] New post 23 Nov 2011, 09:35
I think the answer is E as we do not exactly know who is slower than the other two.
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine' [#permalink] New post 31 Oct 2014, 01:59
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine' [#permalink] New post 31 Oct 2014, 03:13
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enigma123 wrote:
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

A. I only
B. II only
C. III only
D. I or II only
E. I, II, or III


Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.

Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.

There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.

Answer: D.

To elaborate more: the least time one could complete the race is 20/8=2.5 hours, hence \(S+R\geq{5}\). Let's see if Brian could have won the race: best chances to win he would have if he ran at the fastest rate, so he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, but we know that \(S+B\geq{5}\), so even if Brian ran at his fastest rate to win the race, given equation S+R=B+2 can not hold true. Hence Brian could not have won the race.

Hope it's clear.

OPEN DISCUSSION OF THIS QUESTION IS HERE: stephanie-regine-and-brian-ran-a-20-mile-race-stephanie-127050.html
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine'   [#permalink] 31 Oct 2014, 03:13
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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine'

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