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 the 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 :

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

Velocity of girl w.r.t. elevator `=(d)/(t_(1))=v_("ge")`
Velocity of elevator w.r.t. ground `v_(eG)=(d)/(t_(2))` then velocity of girl w.r.t ground
`vec(v)_(gG)=vec(v)_("ge")+vec(v)_(eG)`
i.e., `v_(eG)=v_("ge")+v_(eG)`
`(d)/(t)=(d)/(t_(1))+(d)/(t_(2))`
`(1)/(t)=(1)/(t_(1))+(1)/(t_(2))`
`t=(t_(1)t_(2))/((t_(1)+t_(2)))`