I've been knocking this one around for a little while now but can't seem to reduce it to something simple. It's a relative velocity problem: _________________________________ A river flows at 5ms-1 from west to east between parallel banks which are at a distance 300m apart. A man rows a boat at speed of 3ms-1 in still water. Find the direction in which the boat must be steered in order to cross the river from the southern bank to the northern bank by the shortest possible route. Find the time taken and the actual distance covered by the boat for this crossing. _________________________________ Treating it as a vector problem where the 3ms-1 velocity is at x degrees to the north (upstream) and splitting it into components I came up with a function which I could graph giving an optimal solution of x=36.9 degrees but I need to find a graphical/algebraic solution. Any ideas?