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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink]

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06 Oct 2007, 05:20

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D

E

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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

If Brian ran at the speed of light (8mph) he would have made it in 2.5 hours and the combined time would be 4.5 hours, but this cannot be because 2x2.5 is 5, so Brian must have been running slower than 8mph and in any case the two other runners can be faster than him, but he can never be faster than the two runners.

If Brian ran at the speed of light (8mph) he would have made it in 2.5 hours and the combined time would be 4.5 hours, but this cannot be because 2x2.5 is 5, so Brian must have been running slower than 8mph and in any case the two other runners can be faster than him, but he can never be faster than the two runners.

Don't like to be a nitpicker but, the speed of light is 300,000 kph so it would take him less than one second hence = 0 time.

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

Ans has gotta be D.

Set up equations or rate chart as I like to do. And just try different values for Stephanie and Regine. I recommend rates of 4 and 5 b/c they are divisible by 20.

S || R || B R: 4 || 5 || x
T: Ts || Tr || Ts+Tr-2=Tb
D: 20 || 20 || 20

First plug we get Ts=5 and Tr=4. So Tb=7hrs So Regine won the race.

Now since there is no bearing on S or R we can interchange 4 and 5 so that this time Stephanie wins the race.

So only 2 answer choices left D or E.

Brain will never be able to win the race. (just try more values if ur not certain)