A cyclist leaves a dhaba at 7:00 a.m. riding at 12 km/h. A motorcyclist leaves the same dhaba at 8:30 a.m. on the same road at 30 km/h. At what time does the motorcyclist overtake the cyclist?

Explanation

1. 01

   By 8:30 a.m. the cyclist is $12 \times 1.5 = 18$ km ahead.

2. 02

   The motorcyclist gains at $30 - 12 = 18$ km/h.

3. 03

   Time to close the gap $= \frac{18}{18} = 1$ h, so the overtaking happens at 9:30 a.m.