Question

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

• A. $\frac{t_1 t_2}{t_2 - t_1}$
• B. $\frac{t_1 t_2}{t_2 + t_1}$
• C. $t_1 - t_2$
• D. $ \frac{t_1 + t_2}{2} $

Answer 1

Answer: (B)

Velocity of girl w.r.t. elevator $=\frac{d}{t_{1}}=v_{g e}$
Velocity of elevator w.r.t. ground $v_{e G}=\frac{d}{t_{2}}$ then
velocity of girl w.r.t. ground
$\vec{v}_{g G}=\vec{v}_{g e}+\vec{v}_{e G}$
i.e, $v_{g G}=v_{g e}+v_{e G}$
$\frac{d}{t}=\frac{d}{t_{1}}+\frac{d}{t_{2}}$
$\frac{1}{t}=\frac{1}{t_{1}}+\frac{1}{t_{2}}$
$t=\frac{t_{1} t_{2}}{\left(t_{1}+t_{2}\right)}$