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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 for him to walk up the moving escalator?

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Let `L` be the length of escalator.
Speed of man w.r.t. escalator is `V_(ME)=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))`
`:.` The desired time is `t=L/v_(M)=(t_(1)t_(2))/(t_(1)+t_(2))`
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