Refer `Q.95`. If the man takes `t_1 and t_2` to move to and fro journey respectively, the time taken by him to go downstream (while the man does not swim) is :

Options

A. `(2 t_1 t_2)/(t_(1)+t_(2))`
B. `sqrt(t_1^2 + t_2^2)`
C. `sqrt(t_1 t_2)`
D. `(2 t_1 t_2)/(t_1 - t_2)`

Answer

D

Explanation

velocity of man relative to water = v
Velocity of water flow = u
Velocity of man relative to ground in upstream `= v - u`
Velocity of man relative to ground in downstream `= v + u`
Now for to and fro motion, time taken to cover distance `d` in upstream `t_1 = (d)/(v - u)`
`1/t_(1)=v/d-u/d` ...(i)
And time taken to cover distance `d` in downstream
`t_2 = (d)/( v+ u)`
`(1)/(t_2) = (v)/(d) + (u)/(d)` ...(ii)
Now time taken to cover distance `d` in downstream
When ` v= 0`
`t_3 = (d)/(u)`
Subtracting equation (i) from equation (ii) we get
`(1)/(t_2) - (1)/(t_1) = (2u)/(d)`
Now put value of `u//d` from equation (iii)
`(t_1 - t_2)/(t_1 t_2) = (2)/(t_3) rArr t_3 = (2 t_1 t_2)/(t_1 - t_2)`.