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At a metro station, a girl walks up a st...

At a metro station, a girl walks up a stationary escalator in time `t_1`. If she remains stationary on the escalator, then the escalator take her up in time `t_2`. The time taken by her to walk up on the moving escalator will be

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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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