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

Options

A. `((t_(1)+t_(2)))/(2)`
B. `(t_(1)t_(2))/((t_(2)-t_(1)))`
C. `(t_(1)t_(2))/((t_(2)+t_(1)))`
D. `t_(1)-t_(2)`

Answer

C

Explanation

In this question, 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 `upsilon_(g)=(L)/(t_(1))`
velocity of scalator `upsilon_(e )=(L)/(t_(2))`
Net velocity of the girl `= upsilon_(g)+upsilon_(e )=(L)/(t_(1))+(L)/(t_(2))`
If t is total time taken in covering distance L, then
`(L)/(t)=(L)/(t_(1)+(L)/(t_(2))`
`rArr t=(t_(1)t_(2))/(t_(1)+t_(2))`