Problem:
As Emily is riding her bicycle on a long straight road, she spots Emerson skating in the same direction mile in front of her. After she passes him, she can see him in her rear view mirror until he is mile behind her. Emily rides at a constant rate of miles per hour, and Emerson skates at a constant rate of miles per hour. For how many minutes can Emily see Emerson?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Emily gains on Emerson at the rate of miles per hour. To get from mile behind Emerson to mile in front of him, she must gain mile on him. This takes hour, which is minutes.
Make a chart that shows the position of Emily and Emerson every minutes. Note that for every 5 minutes Emily rides miles per minute minutes mile, and Emerson skates mile. Eventually, Emily will be mile ahead of Emerson. Notice that happens after minutes.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions