You don't really need maths for this as much as just spatial awareness / some sense of galilean relativity.
Imagine you're looking north high above a stationary boat on the mast, and you see a boat moving straight ahead north relative to your compass. You know the motion of that boat as it's given to you. Imagine now that you see it moving north-east, well you know the boat is only moving north as the question gives it to you, but it now appears to be moving east as well. If your boat and that boat were both moving with unknown velocities, you couldn't really say [if the surroundings didnt give it away] what boat was moving in which direction. Since the boat appears to have some motion in the west $\to$ east axis, that would also be seen if your boat was moving the opposite direction in the same axis, which there aren't any restricting conditions for. So then it's reasonable to conclude that that's the way it is.