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 ?

Explanation

Let L be the length of ascalator. Speed of man w.r.t esacalator 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))`