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1. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

A. 30 km/hr

B. 45 km/hr

C. 60 km/hr

D. 75 km/hr

Solution:

\begin{aligned} Let the speed of the slower train be x m/sec \\ Then, speed of the faster train = 2 x m/sec \\ Relative speed = (x + 2 x) m/sec = 3 x m/sec \\ ∴ \frac{100 + 100}{8} = 3 x \\ \Rightarrow 24 x = 200 \\ \Rightarrow x = \frac{25}{3} \\ So, speed of the faster train = \frac{50}{3} m/sec \\ = \frac{50}{3} \times \frac{18}{5} km/hr \\ = 60 km/hr \end{aligned}

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