Problem:
Odell and Kershaw run for minutes on a circular track. Odell runs clockwise at and uses the inner lane with a radius of meters. Kershaw runs counterclockwise at and uses the outer lane with a radius of meters, starting on the same radial line as Odell. How many times after the start do they pass each other?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since Odell's rate is that of Kershaw, but Kershaw's lap distance is that of Odell, they each run a lap in the same time. Hence they pass twice each time they circle the track. Odell runs
as does Kershaw. Because , they pass each other times.
The problems on this page are the property of the MAA's American Mathematics Competitions