X takes 3 hours longer than Y to walk 30 km. If X doubles his speed, he takes 2 hours less than Y. What is the speed of Y?

Explanation

Let speeds be x and y. Equations for time: \frac{30}{x} - \frac{30}{y} = 3 and \frac{30}{y} - \frac{30}{2x} = 2. Adding them eliminates y: \frac{30}{x} - \frac{15}{x} = 5 \implies \frac{15}{x} = 5 \implies x = 3\text{ km/hr}. Then \frac{30}{3} - \frac{30}{y} = 3 \implies 10 - 3 = \frac{30}{y} \implies y = \frac{30}{7} = 4\frac{2}{7}\text{ km/hr}.

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