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Speed of Trains after Crossing

MAT 2018 · Mathematical Skills · Medium · Speed Time Distance

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A train from Mumbai to Pune and another from Pune to Mumbai start at the same time, cross one another en route and reach their destinations in 4 hours and 1 hour, respectively, after crossing. If the first train was travelling at 24 kmph, at what speed was the second train travelling?

  1. A.

    12 kmph

  2. B.

    48 kmph

  3. C.

    60 kmph

  4. D.

    72 kmph

Answer

B

Explanation

The standard relationship for speeds of two bodies after crossing each other is: S1S2=T2T1\frac{S_1}{S_2} = \sqrt{\frac{T_2}{T_1}} Given S1=24S_1 = 24, T1=4T_1 = 4 hours, T2=1T_2 = 1 hour. 24S2=14=12  ⟹  S2=48 kmph.\frac{24}{S_2} = \sqrt{\frac{1}{4}} = \frac{1}{2} \implies S_2 = 48 \text{ kmph}.

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