Preeti reached the metro station and found that the escalator was not working. She walked up the stationary…

Let $d$ be the displacement of the escalator.

Velocity of girl w.r.t. elevator $=\frac{d}{t_1}={\mathrm{v}}_{ge}$
Velocity of elevator w.r.t ground ${\mathrm{v}}_{eG}=\frac{d}{t_2}$

Then velocity of girl w.r.t ground
${\overrightarrow{\mathrm{v}}}_{gG}= {\overrightarrow{\mathrm{v}}}_{ge}+{\overrightarrow{\mathrm{v}}}_{eG}$
i.e., $V_{gG}=V_{ge}+V_{eG}$
$\frac{d}{t}=\frac{d}{t_1}+\frac{d}{t_2}$
$\frac{1}{t}=\frac{1}{t_1}+\frac{1}{t_2}$
$t=\frac{t_1 t_2}{\left(t_1+t_2\right)}$