Question:

A man stands at a point A on the bank of a straight river 1km wide which is flowing at speed of 12km/h. To reach point B, 10km down the river on the other side, he first rows the boat to a point P on the opposite side and then walks the remaining distance to B. He can row at a speed of 3 km/h (in still water) and he walks 6km/h. The river flows at 12 km/h.

Determine the angle θ that would get the man to point B the fastest.Work:

Let O be the place where the boat starts. Consider point P as if it were moving towards O at 12km/h. This makes the water stationary.

equations:

total time =

I then take the derivative of this which is and set this equal to 0. Then solving for θ I get

problem: none of these angles make sense becaue they need to be between and 0.