Very similar to the shortest path ones already mentioned: A person is on the shore at a perpendicular distance $d_1$ from the shore and wants to rescue a person drowning at a perpendicular distance $d_2$ from the shore and a distance $\ell$ from the first person's position on the shore (usually that's sketched); they can run at speed $v_1$ and swim at speed $v_2$. What path should they take to the drowning person in order to rescue them as quickly as possible?