Making races equal

If you ever watch track and field at the Olympics, you'll notice that the starting points of the runners are not even if the race is run on a curve and the runners have to run in lanes. This is to offset the fact that the distances along each lane are unequal on a curve. To see this effect, consider two runners, each of whom runs at a speed of \(7~\mbox{m/s}\). The runners run on a circular track. The radius of the inside lane is \(50~\mbox{m}\), and the radius of the outside lane is \(51~\mbox{m}\). By how many seconds will the inside runner beat the outside runner if they each run once around the track?

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