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Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_{1}$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_{2}$. The time taken by her to walk up on the moving escalator will be:
Explanation
Velocity of preeti w.r.t. elevator $v_{1} = d/t_{1}$ Velocity of elevator w.r.t. ground $v_{2} = d/t_{2}$ then velocity of preeti w.r.t. ground $v = v_{1} + v_{2}$ $d/t = d/t_{1} + d/t_{2} \Rightarrow 1/t = 1/t_{1} + 1/t_{2}$ $\therefore t = t_{1}t_{2}/(t_{1}+t_{2})$ (time taken by preeti to walk up on the moving escalator)