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The speeds of two cyclists are in the ratio 4:3. If the slower cyclist has a 15 km head start and his speed is 18 km/h, how far will the faster cyclist travel to overtake him?

1. 50 km
2. 60 km
3. 75 km
4. 90 km

Correct answer: 60 km

Solution

The slower cyclist's speed is 18 km/h, so the faster cyclist's speed is \(18\times\frac{4}{3}=24\) km/h. Relative speed is \(24-18=6\) km/h, so time to catch up is \(15/6=2.5\) hours. In that time, the faster cyclist travels \(24\times2.5=60\) km.

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