Both the times are same.
Work Step by Step
The plane at rest has the velocity relative to earth equal to zero. So the velocity of the plane at rest is equal to the velocity of the earth. When the plane takes off in the direction of the velocity opposite to the rotation of the earth, the speed of the plane is already lesser than the velocity of what it would have been if the plane had taken off in the direction same as that the rotation of the earth. Since the relative velocity with respect to the earth is the same, so the times are same too.