A person standing on the escalator takes time $t_{1}$ to reach the top of a tower when the escalator is moving. He takes time $t_{2}$ to reach the top of the tower when the escalator is standing. How long will he take if he walks up a moving escalator?

t_{2} - t_{1}

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t_{1} + t_{2}

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t_{1} t_{2} / (t_{1} - t_{2})

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t_{1} t_{2} / (t_{1} + t_{2})

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Solution

The correct option is D $t_{1} t_{2} / (t_{1} + t_{2})$
Let distance to be traversed = x.
Speed of escalator $= \frac{x}{t_{1}}$
Speed of man walking $= \frac{x}{t_{2}}$
When the man is walking on a moving escalator, speed is $= x (\frac{1}{t_{2}} + \frac{1}{t_{1}}) = x \frac{(t_{1} + t_{2})}{t_{1} t_{2}}$
Time taken is distance by speed $= \frac{x}{v} = \frac{t_{1} t_{2}}{t_{1} + t_{2}}$
Hence option D is correct.

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Similar questions

A person walks up a stationary escalator in $t_{1}$ second. If he remains stationary on the escalator, then it can take him up in $t_{2}$ second. If the length of the escalator is L, then how much time would it take him to walk up the moving escalator?