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

BTGmoderatorLU 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

We see that since nobody ran faster than 8 miles per hour, then each of them took more than 20/8 = 2.5 hours to complete the 20-mile race.

If Stephanie took 2.6 hours and Regine took 2.7 hours to complete the race, then Brian took 2.6 + 2.7 - 2 = 3.3 hours to complete the race. In this case Stephanie is the winner of the race.

If we switch Stephanie’s time with Regine’s, then Regine is the winner of the race.

Finally, if we let Stepanie’s time = 2.5 + s and Regine’s time = 2.5 + r for some positive numbers s and r, then Brian’s time = 2.5 + s + 2.5 + r - 2 = 3 + s + r. We see that Brian took more time than either Stepanie or Regine to complete the race, which means he could never be the winner of the race. So only Stephanie or Regine could be the winner of the race.

Answer: D