Question

Two persons `P` and `Q` crosses the river starting the 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 person is `5kmph` w.r.t river. If the two persons reach the point `B` in the same time, then the speed of walk of `Q` is .

Answer 1

`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+x/V_(man),But x=V_(w)d/V_(B)`
`d/4=d/5+(V_(W)d)/(V_(B)V_(man)),d/4=d/5+(3d)/((5)V_(man))`
`1/4-1/5+(3)/(5V_(man)), 1/20=3/(5V_(man))`
`V_(man)=((3)(20))/5=12kmph`