A swimmer crosses a flowing stream of width .d.to and fro in time t_(1). The time taken to cover the same distance up and down the stream is t_(2). If t_(3) is is the time the swimmer would take to swim a distance 2d in still water, then

A swimmer crosses a flowing stream of width .d.to and fro in time t_(1

1.	A swimmer crosses a flowing stream of width .d.to and fro in time t_(1). The time taken to cover the same distance up and down the stream is t_(2). If t_(3) is is the time the swimmer would take to swim a distance 2d in still water, then
Answer» SOLUTION :Let v be the river velocity and u the velocity of SWIMMER in still water. Then `t_(1) = 2((d)/(sqrt(u^(2) - v^(2))))` …..(i) `t_(2) = (d)/(u + v) + (d)/(u-v) = (2ud)/(u^(2) - v^(2))` ….(ii) and `t_(3) = (2d)/(u)` ….(iii) from equations (i), (ii) and (iii) `t_(1)^(2) = t_(2)t_(3) rArr t_(1) = sqrt(t_(2)t_(3))`