Question

At a metro station, a girl walks up a stationary escalator in time $t_1$, If she remains stationary on the escalator, then the escalator take her up in time $t_2$. The time taken by her to walk up on the moving escalator will be

• A. $(t_1 + t_2)/2$
• B. $t_1 t_2 /(t_2 — t_1)$
• C. $t_1t_2/(t_2 + t_1)$
• D. $t_1 - t_2$

Answer 1

Answer: (C)

We have to find net velocity with respect to the Earth that will be equal to velocity of the girl plus velocity of escalator. Let displacement is $L$, then
Velocity of girl $v_g = \frac{L}{t_1}$
Velocity of escalator $v_e = \frac{L}{t_2}$
Net velocity of the girl $ = v_g + v_e = \frac{L}{t_1} + \frac{L}{t_2}$
If $t$ is total time taken in covering distance $L$, then
$\frac{L}{t} +\frac{L}{t_1} + \frac{L}{t_2}$
$\Rightarrow t = \frac{t_1t_2}{t_1 + t_2}$