A fair game

Distance runners often run around an approximately circular trajectory. However, since some runners are running at a larger radius than others, they must be given an advantage in the beginning so that the race is fair.

If the path of the runner running at a greatest radius of \(20~\mbox{m}\) is \(100~\mbox{m}\) long, how far behind in m should the runner at the smallest radius start? The smallest radius is \(15~\mbox{m}\).

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