Question: Boat A's position is given by x(t)=3-t, y(t)=2t-4 where the distance units are kilometres and the time units are hours. Boat B's position is given by x(t)=4-3t, y(t)=3-2t. Then I figured out that the initial position of each boat is: A: (3,-4), B: (4,3) And the velocity vector of each boat is: A: (-1, 2), B: (-3, -2) So at what time are the boats closest to each other? I know the two lines meet at one point, but since the the speed at which each boat is moving is different, one boat will get to the intersect earlier than the other, and therefore this will not work. So how do I find when the boats are closest?