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Hi Paul

I regret that the misleading element here is, unfortunately, you. The answer above is correct, but let me add further information, which might help you to appreciate why you are mistaken.

If you fly "with" the wind - i.e. in the direction of the Earth's rotation - then you will do less work against the headwind and cover the ground more rapidly. Conversely, if you fly into the headwind, for every mile you move forward, the wind moves you back a set distance; hence it's harder to fly west than east.