Two trains, X and Y, start at the same time from Delhi and Mumbai towards each other. After meeting, train X takes 6 hours to reach Mumbai, and train Y takes 8 hours to reach Delhi. If train X's speed is 60 km/h, what is the speed of train Y?
\(30\sqrt{3}\) km/h
When two bodies start together and move towards each other, after meeting the ratio of their speeds equals \(\frac{V_X}{V_Y} = \sqrt{\frac{t_Y}{t_X}}\), where \(t_X\) and \(t_Y\) are the times taken after meeting.
Here \(t_X = 6\) hours and \(t_Y = 8\) hours, so \(\frac{V_X}{V_Y} = \sqrt{\frac{8}{6}}\).
Therefore \(V_Y = V_X \times \sqrt{\frac{6}{8}} = 60 \times \sqrt{\frac{3}{4}} = 60 \times \frac{\sqrt{3}}{2}\).
\(V_Y = 30\sqrt{3}\) km/h.
Hence, the speed of train Y is \(30\sqrt{3}\) km/h.
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