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Cyclists on one road

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$2$ cyclists start at the same moment from towns $75$ km apart and ride toward each other on the same road, one at $12$ km/h and the other at $18$ km/h, each at a constant speed. After how many hours do they meet? Give the answer as a fraction in lowest terms.

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Hint

Think of the gap between them shrinking at a single combined speed.

Solution

The gap closes at $12 + 18 = 30$ km per hour.
They meet when the whole $75$ km has closed, which takes $\frac{75}{30}$ hours.
In lowest terms $\frac{75}{30} = \frac{5}{2}$ , so the answer is $\frac{5}{2}$ .

Answer: $\frac{5}{2}$

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