Referring to `Q.95`, the time taken by the man in moving to and fro through equal distance when there is no flow of water is :

Options

A. `(t_1 + t_2)/(2)`
B. `(t_1 t_2)/(t_1 - t_2)`
C. `(4 t_1 t_2)/(t_1 + t_2)`
D. `sqrt(t_1 t_2)`

Answer

C

Explanation

From previous solutions,
`(1)/(t_1) = (v)/(d) -(u)/(d)`…(i)
`(1)/(t_2) = (v)/(d)+(u)/(d)`…(ii)
Now time taken to cover distance `2d` when there is no water flow i.e., `u = 0`
`t_3 = (2d)/(v)` …(iii)
Adding equation (i) and (ii), we get
`(1)/(t_1) + (1)/(t_2) = (2v)/(d)`
Put value of `v//d` from equation (iii)
`(t_1 + t_2)/(t_1 t_2) = (u)/(t_3)`
`t_3 = (4 t_1 t_2)/(t_1 + t_2)`.