Buses leave a depot every 15 minutes and run along a straight highway at a constant speed of 16 km/h. A cyclist is riding towards the depot from the opposite direction on the same highway. He observes that buses cross him at regular intervals of 12 minutes. Assuming both maintain uniform speeds, what is the speed (in km/h) of the cyclist?
4
Buses leave every 15 minutes at 16 km/h, so they are 16 × \(\frac{15}{60}\) = 4 km apart on the road.
The cyclist meets a bus every 12 minutes, so buses and cyclist together close a 4 km gap in \(\frac{12}{60}\) h: relative speed = 4 ÷ 0.2 = 20 km/h.
They move towards each other, so cyclist's speed = 20 − 16 = 4 km/h.
Hence, the answer is 4.
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