The problem of cycling on 4 circles.

This is a motion problem from the 2007 International Mathematical Science Olympiad for 5th and 6th graders. Can you solve it in 5 minutes?

Topic:

A park has four circular paths converging at a single point, as shown in the diagram below. Four cyclists start simultaneously at 12 noon from the converging point. Their cycling speeds per hour are 6 miles, 9 miles, 12 miles, and 15 miles, respectively.

Ask all four people at what time they meet at the starting point on the fourth occasion, knowing that the circumference of each circle is 1/3 mile.

Instructions on how to solve

Tran Phuong (Deputy Director of the Talent Development Center)

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