Three runners start together from a point of a 1.2 km track and run the same way at 3 m/s, 5 m/s and 9 m/s. How far from the start, measured along the track, are they when all three first come together?

Question

Accepted Answer

600 m. Pairwise gains 2, 4 and 6 m/s give meeting intervals of 600 s, 300 s and 200 s; all three together first at 600 s. The slowest has run 3×600=1800 m =11/2 laps, so they meet 600 m from the start.

Three runners start together from a point of a 1.2 km track and run the same way at 3 m/s, 5 m/s and 9 m/s. How far from the start, measured along the track, are they when all three first come together?

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