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Two cyclists and a pedestrian in a circular runway

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October 13, 2010
algebra unsolvedalgebra

Problem Statement

Two cyclists leave simultaneously a point PP in a circular runway with constant velocities v1,v2(v1>v2)v_1, v_2 (v_1 > v_2) and in the same sense. A pedestrian leaves PP at the same time, moving with velocity v3=v1+v212v_3 = \frac{v_1+v_2}{12} . If the pedestrian and the cyclists move in opposite directions, the pedestrian meets the second cyclist 9191 seconds after he meets the first. If the pedestrian moves in the same direction as the cyclists, the first cyclist overtakes him 187187 seconds before the second does. Find the point where the first cyclist overtakes the second cyclist the first time.
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