the surface of the earth with you on it is moving around a thousand miles per hour to the east relative to the center of the Earth.

Even at 45 degrees latitude, the Earth's surface is moving 700 miles per hour to the east.

So it kind of seems like it should be faster for airplanes to fly west.

I mean their destination is literally spinning towards them.

At the same time, however, they're spinning away from their destination.

When we say the earth is going a thousand miles per hour to the east, 

that means that the ground, and airplanes on the ground, and even the air above the ground are also moving a thousand miles per hour to the east.

For an airplane to get anywhere, it has to start moving relative to the ground and through the air, at something like a hundred or so miles per hour.

So when it flies east, it's actually moving a thousand plus a hundred mile an hour to the east.

And when it flies west, it's actually moving a thousand minus a hundred miles an hour to the east. 

Yes! To go west, you go east just slower than the Earth is going east.

Unless you're within 10 or so miles of the poles in which case a brisk westward walk will take you legitimately west.

That said a plane do often take different amounts of time to fly the same route in different directions.

Because of wind in the upper atmosphere like the jet stream that they either have at their tail or have to fly into.

The prevailing direction of these winds is largely caused by the Coriolis effect,

which is caused by the fact that different parts of the Earth are moving east at different speeds,

which happens because the Earth is round and spinning.

So airplane travel times are influenced by the rotation of the Earth, just not in a straightforward way.

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