A boat moves at $4\ \text{m/s}$ in still water. Its rower keeps it pointing straight across a river that flows at $3\ \text{m/s}$, as the figure shows. How fast does the boat move over the river bed, and in which direction?

Fig. 1: A river flowing to the right at 3 m/s, and a boat pointing straight across at 4 m/s through the water.