How much does the Earth's rotation affect aircraft travel times?

Flying to the Mid-East takes 6 hours, the return flight is 7 hours.
Now I know that aircraft are always susceptible to the speed of air around them. So if you have a 100 MPH tailwind theoretically you gain an extra 100 MPH relative to ground travel.
I have done a 50 minute Gatwick-Inverness flight which usually takes 1 hr 30 on a Bae 146 but for an 140 MPH tailwind.
However movement of air may follow patterns but there is no guarantee eitherway of a headwind or a tailwind. It’s just something that happens when the weather feels like doing it.
Air is though subject to the same gravitational forces as we humans. So does it automatically create a headwind when you fly counter-rotation and a tailwind when with rotation?

Is this why the outbound flight is an hour shorter than the inbound?

The earth’s rotation, in and of itself, has no effect on aircraft travel time since the atmosphere rotates with the earth.

An indirect effect is that rotation does affect wind direction and that does affect travel time.

The prevailing winds are westerly so in going east you are generally going with the wind and going west against it.

**David **got it right. A more detailed explanation can be found here.

Prevailing wind direction varies with range of latitude.

True, but I think from here to the Mid east is in the westerlies zone.