2012-03-20 09:00:18

Alexandra drove 150 miles to her aunt's house. If she had driven 10 miles per hour faster, she would have gotten there a half hour faster. What was her speed for the journey?

A) 40 mph
B) 50 mph
C) 55 mph
D) 60 mph
E) 100 mph

The correct answer is B

Explanation: The best approach to this question is to plug in the answer choices. Start with 55 mph. If Alexandra drove 150 miles at 55 mph, she would have gotten to her aunt’s house in just under 2 hours and 44 minutes (from 150/55 = 2.72 hours). If she went 10 mph faster than 55 mph, she would have gone 65 mph and gotten to her aunt’s house in 2 hours and 18 minutes, which is less than a half hour difference. Anything faster than that is going to have even less of time difference because of a 10 mph speed increase, so eliminate C, D, and E. Move on to B.

If Alexandra drove 150 miles at 50 mph, she would have gotten to her aunt’s house in 3 hours. If she’d gone 10 mph first, she would have gone 60 mph. This would get her to her aunt’s house in 2.5 hours, which is a ½ hour shorter, making choice B the right answer.