Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie

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

Time (s) + time (r) = time (b) +2

d=20

If no one ran faster than 8 miles/hour than no one completed the race in under 2.5 hours (time = distance/rate ===> time = 20/8 ===> time = 2.5 hours)

If S+R = B+2, Brian's time will always be greater than S or R. Because no one finishes in under 2.5 hours we can rule out maximum speeds. For example, Brian can not finish in 2.5 hours because S and R would have to have a combined time of 4.5 hours which we know is not possible because 4.5 combined would mean both of them ran it in under 2.5 hours. If Brian finished in 3 hours S and R's time could have been 2.5 each meaning their combined time is exactly two hours greater but their times separately are less than Brian's. The only way the equation can hold true is if Brian's time is equal to or greater than three in which case either S or R (or both) always run in less time.

ANSWER: (D) I or II only