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 - t _(1))`
C. `t _(1) t _(2) //(t_(2) + t _(1))`
D. `t _(1) - t _(2)`

Answer

C

Explanation

Net velocity with respect to the Earth that will be equal to velocity of the girl plus velocity of esaclator.
Let displacemtn is L, then
velocity of girl `v _(g) = (L)/(t _(1)) `
velocity of escaltoor `v _(e) = (L)/(t _(2))`
Net velocity of the girl, `v =v _(g) + v _(e) = (L)/(t_(1)) + (L)/(t_(2)) ...(i)`
If t is total time taken in covering distance L, then `v = L/t`
Using in (i) `L/t = (L)/(t _(1)) + (L)/(t _(2)) implies t = (t_(1) t_(2))/(t _(1) + t _(2))`