Two persons P and Q crosses the river starting from point A on one side to exactly opposite point B on the other bank of the river. The person P crosses the river in the shortest path. The person Q crosses the river in shortest time and walks back to point B. Velocity of river is 3 kmph and speed of each boat is 5 kmph w.r.t river. If the two persons reach the point B in the same time, then the speed of walk of Q is

Explanation

`t_(p) =d/sqrt(V_(B)^(2)-V_(W)^(2)) =d/sqrt(5^(2)-3^(2))=d/4`
`t_(Q) =d/V_(B) =d/5, t_(p) =t_(Q) + Deltat`
`d/4 =d/5 +(V_(w)d)/(V_(B)V_("man")) , d/4 =d/5 +(3d)/(5 V_("man"))`
`1/4-1/5 =3/(5 V_("man")) =3/(5V_("man")), 1/20 =3/(5V_("man"))`
`V_("man") -((3)(20))/5 =12` kmph