10.2#12

I am confused about this one because it only gives one value (51 miles/hour). I know that the wind velocity vector and the desired vector are perpendicular to each other because the wind is directly from the west and the two towns are directly north/south of each other, but I don't know how to solve for another speed if I don't have a time or distance or anything.

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Well, you are give another direction though, which is that they're flying "northwest", in which the component of the velocity in the north direction exactly balances the component in the west direction. They want to travel directly north, so how can they balance the wind exactly with the west component of their velocity?