Even if we don’t realize it, the Earth revolves around its axis from west to east, at a speed of 1,670 km per hour at the equator. Shouldn’t it, then, be faster and cheaper to fly west – as our plane will sort of “beat” the time, while approaching our destination?

The short answer is no: even the plane, with the ground from which it takes off and like the Earth’s atmosphere in which it flies, is influenced by the rotation, and then moves away from its destination, while this tries to approach it.

For the plane to be able to move actively, it must begin to move relatively on the ground, and acquire a speed of at least 160 km per hour (this is at least in the case of small aircraft, because the “giants” exceed 300). If the plane moves eastward, this little extra speed is added to that 1,670 miles an hour before. If it goes west, because it’s “dragged” in the opposite direction along with the atmosphere, it’s like it’s going east anyway, minus that hundred miles an hour. In practice, to go west you move east anyway, and in any case slower than the Earth’s rotation speed (unless you are at the poles).

It is all explained in this video: https://www.youtube.com/watch?v=3gNkgj9h2oM
Enjoy!