Problem:
Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run meters. They next meet after Sally has run meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
When they rst meet, they have run a combined distance equal to half the length of the track. Between their rst and second meetings, they run a combined distance equal to the full length of the track. Because Brenda runs at a constant speed and runs meters before their rst meeting, she runs meters between their rst and second meetings. Therefore the length of the track is meters.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions