At a metro station, a girl walks up a stationary escalator in time $t_1$. If she remains stationary

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

Professor PC Thomas Classes · Answer

(c) : Let $L$ be the length of escalator. Velocity of girl w.r.t. escalator, $v_{g e}=\frac{L}{t_1}$ Velocity of escalator, $v_e=\frac{L}{t_2}$ Velocity of girl w.r.t. ground would be \ $ v_g=v_{g e}+v_e=L\left(\frac{1}{t_1}+\frac{1}{t_2}ight) $ \  $	herefore \quad$ The desired time is $t=\frac{L}{v_g}=\frac{L}{L\left(\frac{1}{t_1}+\frac{1}{t_2}ight)}=\frac{t_1 t_2}{t_1+t_2}$