2006 AMC 10A Problems/Problem 15
Problem
Odell and Kershaw run for 30 minutes on a circular track. Odell runs clockwise at 250 m/min and uses the inner lane with a radius of 50 meters. Kershaw runs counterclockwise at 300 m/min and uses the outer lane with a radius of 60 meters, starting on the same radial line as Odell. How many times after the start do they pass each other?
Solution
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- please note that this is this solution has not been confirmed but is only my own solution to the problem.
We know that Odell and Kershaw meet after they run a total of one circle together. Odell runs at 250m/min for 30 mins in a circle of length of 100pi, and that Kershaw runs at 300m/min for 30 mins in a circle 120pi in length. Both Odell and Kershaw run 23.8 laps around their respective circles. together they run 47.6 laps. Therefore, they meet a total of 47 times.
(D) 47
