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 walk up on the moving escalator will be

• A. $t_1-t_2$
• B. $\frac{t_1+t_2}{2}$
• C. $\frac{t_1{t}_2}{t_2-t_1}$
• D. $\frac{t_1{t}_2}{t_1+t_2}$

Answer 1

The correct option is D $\frac{t_1{t}_2}{t_1+t_2}$

$t_1=$ time taken at stationary escalator
$t_2=$ time taken at moving escalator
$t^{\prime }=$ time taken in walking up the moving escalator
$d=$ displacement of escalator
$V_1=$ Velocity of Preeti
$V_2=$ Velocity of escalator
$(V_1+V_2)=\frac{d}{t^{\prime }}$, as $V_1=\frac{d}{t_1},V_2=\frac{d}{t_2}$
$\frac{d}{t_1}+\frac{d}{t_2}=\frac{d}{t^{\prime }}\Rightarrow t^{\prime }=\frac{t_1{t}_2}{t_1+t_2}$