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Two cyclists start from the same point on a circular track of length 900 m at 7:00 a.m. and ride in opposite directions. Their speeds are 6 km/h and 9 km/h respectively. At what time will they meet for the fourth time?

1. 7:15:18 a.m.
2. 7:14:24 a.m.
3. 7:30:24 a.m.
4. 7:36:18 a.m.

Correct answer: 7:14:24 a.m.

Solution

Their relative speed is \(6+9=15\) km/h = \(250\) m/min. On a 900 m track, they meet every \(900/250=3.6\) minutes = 3 min 36 s. The fourth meeting occurs after \(4\times 3.6=14.4\) minutes, i.e. at 7:14:24 a.m.

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