Which Trip Would Take Longer?

As the owner and pilot of a light aircraft, I can tell you this: We use three different speed:

IAS: Indicated air speed. What our instrument indicated based on the pitot tube pressure.

TAS: True air speed, compensated for the fall of pressure in altitude. That is, the speed relative to the earth surface. The higher we fly, the faster we fly, and

SOG: Speed over the ground, compensated for the wind component.

If there is no wind, it means that the air rotates with the earth at exactly the same speed. Hence a flight over an equal distance westward or eastward takes exactly the same time on a windless day.

But here is an interesting question: If you fly from A to B then back from B to A on a windless day, will it take the same time, more time, or less time than if you fly from A to B in a headwind, then from B to A in a tailwind?

Most will answer that it takes the same time as what is lost one way is then gained the other way. That is not true. Do the math and you will find out the a return trip will always take longer time on a windy day, whatever its direction.

That question is actually what we are asked when we pass the navigation assessment to become a pilot.

Same time. Al speeds of flight are in relation to the planet surface. The rotation may be ignored as all elements are experiencing the same rotation.

Are you flying in the prevailing winds or the trade winds? The only way the Earth's direction of rotation would make a difference in the problem.