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_1t_2)/(t_2 - t_1)`
C. `(t_1 t_2)/(t_2 + t_1)`
D. `t_1 - t_2`

Answer

C

Explanation

h is height curved to reach from one floor to other floor
Speed of walking = `(h)/(t_1) = v_1`
Speed of escalator `= (h)/(t_2) = v_2`
So time taken when escalator is running, she is also walking on it ` = t = (h)/(v_1 + v_2)`
`1/t = (v_1 + v_2)/(h) = (1)/(t_1 ) + (1)/(t_2) rArr t = (t_1 t_2)/(t_1 + t_2)`