A motorboat moves at $5\ \text{m/s}$ in still water. It crosses a river $120\ \text{m}$ wide that flows at $3\ \text{m/s}$, pointing straight across all the way, as the figure shows. How long does the crossing take, and how far downstream does the boat land?

Fig. 1: A river 120 m wide flowing at 3 m/s. A boat at A points straight across at 5 m/s. B is directly opposite A.