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:
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Solution:
At mph, Qiang travels the first miles in = hour. If he had driven the first half hour at mph, he would have traveled miles. So he needs to make up the extra miles in the second part of the trip, in which he is driving mph faster than his overall average. He will require = hours to make up the extra miles. In that time, he will travel miles.
Let represent the time in hours for the second part of the trip. The distance for the first part of the trip is miles, and the distance for the second part of the trip is the average speed, mph, times . The distance for the entire trip is the average speed, mph, times the total time, . Thus
and it follows that = 2 hours. The distance traveled in hours at mph is miles.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions