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Bicyclists on a Track

Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider.

First Course in Algebra, Hawkes et al., 1909

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"Bicyclists on a Track," Convergence (February 2008)