Train X crosses a man standing on the platform in 24 seconds and train Y crosses a man standing on the platform in 18 seconds. They cross each other while running in opposite directions in 20 seconds. What is the ratio of speed of X to speed of Y?

Explanation

Let the speeds be V_x and V_y. The lengths are L_x = 24 V_x and L_y = 18 V_y. When crossing each other, time t = \frac{L_x + L_y}{V_x + V_y} = 20. So, \frac{24 V_x + 18 V_y}{V_x + V_y} = 20 \implies 24 V_x + 18 V_y = 20 V_x + 20 V_y \implies 4 V_x = 2 V_y \implies \frac{V_x}{V_y} = \frac{1}{2}.

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