Problem:
Qiang drives miles at an average speed of miles per hour. How many additional miles will he have to drive at miles per hour to average miles per hour for the entire trip?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
For the first miles, Qiang drove for hour. Let be the distance that Qiang must drive to satisfy the condition. It will take him hours to drive this distance. The total trip is now miles. We know the average speed is miles per hour, so this will take him hours. Setting the two times equal to each other, we get
Cross-multiplying and simplifying yields
Solving for , we get
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions