Problem:
A straight one-mile stretch of highway, feet wide, is closed. Robert rides his bike on a path composed of semicircles as shown. If he rides at miles per hour, how many hours will it take to cover the one-mile stretch?
Note: mile feet
Answer Choices:
A.
B.
C.
D.
E. <
Solution:
Each semicircle moves Robert feet ahead, so he would have to ride semicircles to cover mile. Riding semicircles is equal to the distance of full circles. Each circle has a circumference of , so Robert rides feet. Converting to miles, that is miles. Since he is riding at miles per hour, it will take him hours.
Each semi-circular path is times as long as the straight path. Since the straight path would take hour to ride, the curved path will take hours to ride.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions