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

Let the total length of the path covered by the escalator be d.
Let the speed of the girls when escalator is stationary be
`v_(1)=(d)/(t_(1))`
Let the speed of escalator be `v_(2)=(d)/(t_(2)`
Let the time taken by the girls to reach the metro station while walking on the moving escalator be t.
Velocity of the girl on the moving escalator, `v=(d)/(t)`
`v=v_(1)+v_(2)`
`(d)/(t)=(d)/(t_(1))+(d)/(t_(2))`
`(1)/(t)=(1)/(t_(1)+(1)/(t_(2))rArr t=(t_(1)t_(2))/(t_(1)+t_(2))`