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A person walks up a stationary escalator...

A person walks up a stationary escalator in time `t_(1)`. If he remains stationary on the escalator, then it can take him up in time `t_(2)` .How much time would it take him to walk up the moving escalator ?

Text Solution

Verified by Experts

Let L be the length of escalator
Speed of man w.r.t escalator is `v_(rms) =L/t_(1)`
Speed of escalator `v_(e) =L/t_(2)`
Speed of man with respect to ground would be
`v_(m) =v_(me) +v_(e) = L(1/t_(1) + 1/t_(2))`
`therefore` The desired time is `t=L/v_(m) =(t_(1)t_(2))/(t_(1)+t_(2))`
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