IMO 1984 LL SPA51

Origin: SPA

Problem

Two cyclists leave simultaneously a point P in a circular run- way with constant velocities v1, v2 (v1 > v2) and in the same sense. A pedestrian leaves P at the same time, moving with velocity v3 = v1+v2 . If the pedestrian and the cyclists move in opposite directions, the pedes- trian meets the second cyclist 91 seconds after he meets the first. If the pedestrian moves in the same direction as the cyclists, the first cyclist overtakes him 187 seconds before the second does. Find the point where the first cyclist overtakes the second cyclist the first time.