Problem:
Mr. Earl E. Bird leaves his house for work at exactly 8:00 A.M. every morning. When he averages 40 miles per hour, he arrives at his workplace three minutes late. When he averages 60 miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should Mr. Bird drive to arrive at his workplace precisely on time?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the number of hours Mr. Bird must travel to arrive on time. Since three minutes is the same as 0.05 hours, . Thus,
The distance from his home to work is miles. Therefore, his average speed should be miles per hour.
\section*{OR}
Let be the distance from Mr. Bird's house to work, and let be the desired average speed. Then the desired driving time is . Since is three minutes too short and is three minutes too long, the desired time must be the average, so
This implies that .
The problems on this page are the property of the MAA's American Mathematics Competitions