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 $=\frac{d}{t_1}=v_{ge}$
Velocity of elevator w.r.t. ground $v_{eG}=\frac{d}{t_2}$ then
velocity of girl w.r.t. ground
${\vec{v}}_{gG}={\vec{v}}_{ge}+{\vec{v}}_{eG}$
i.e, $v_{gG}=v_{ge}+v_{eG}$
$\frac{d}{t}=\frac{d}{t_1}+\frac{d}{t_2}$
$\frac{1}{t}=\frac{1}{t_1}+\frac{1}{t_2}$
$t=\frac{t_1{t}_2}{\left(t_1+t_2\right)}$