Cycling problem on 4 circles

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

Topic:

A park has 4 circular paths converging at 1 point as shown in the diagram below. Four cyclists start at 12 noon at the converging point. The hourly cycling speeds of each cyclist are 6 miles, 9 miles, 12 miles, 15 miles.

Ask all 4 people at what time meet at the starting point on the 4th time knowing that the circumference of each circle is 1/3 mile.

Instructions for solving

Tran Phuong (Deputy Director of Talent Development Center)

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