Problem:
Andrea and Lauren are kilometers apart. They bike toward one another with Andrea traveling three times as fast as Lauren, and the distance between them decreasing at a rate of kilometer per minute. After minutes, Andrea stops biking because of a flat tire and waits for Lauren. After how many minutes from the time they started to bike does Lauren reach Andrea?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the rate that Lauren bikes, in kilometers per minute. Then , so . In the first minutes, the distance between Andrea and Lauren decreases by kilometers, leaving Lauren to travel the remaining kilometers between them. This requires
minutes, so the total time since they started biking is minutes.
The problems on this page are the property of the MAA's American Mathematics Competitions