A swimmer crosses a flowing stream of width d to and fro in time t1 .The time taken to cover the same distance up and down the stream ist2 . Then the time the swimmer would take to swim a distance 2 d in still water is

Let u be the velocity of swimmer and v be the velocity of river flow. Then        t1=2du2−v2 and  t2=du−v+du+v=2udu2−v2 If t is the time taken by swimmer to swim a distance 2 d still water, then t=2du     t2×t=2udu2−v2×2du=4d2u2−v2 From above, t2×t=t12   or  t=t12/t2