Q. Is air travel time the similar whether or not the plane is flying with or against the rotation of the Earth?

Answer:-

All air travel gets the earth's rotation into account. Flights from east to west acquire less time in absolute terms having nothing to do with time zones. The reverse is true with west to east flights as well as even north-south flights must calculate the amount of rotational deviance while the aircraft is in flight. Extensive range naval cannons have been computing the earth's rotation under the projectile in aiming calculations for more than a century. Satellites in synchronous orbit that appear stationary are actually travelling at the earth's rate of rotation.