Looking for classes? Ksquare Career Institute, Bengaluru →
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
Speeds add, so reciprocals of times add.
Detailed Solution
Velocity of girl w.r.t. escalator $v_{ge} = \frac{d}{t_1}$
Velocity of escalator w.r.t. ground $v_{eG} = \frac{d}{t_2}$
Velocity of girl w.r.t. ground: $\vec{v}_{gG} = \vec{v}_{ge} + \vec{v}_{eG}$
$\frac{d}{t} = \frac{d}{t_1} + \frac{d}{t_2} \Rightarrow \frac{1}{t} = \frac{1}{t_1} + \frac{1}{t_2}$
$t = \frac{t_1t_2}{(t_1 + t_2)}$