Why do aeroplanes take longer to fly west than east?

Every planet/moon has global wind that are mostly determined by the way the planet/moon rotates and how evenly the Sun illuminates it. On the Earth the equator gets much more Sun than the poles. resulting in warmer air at the equator than the poles and creating circulation cells (or "Hadley Cells") which consist of warm air rising over the equator and then moving North and South from it and back round.

The Earth is also rotating. When any solid body rotates, bits of it that are nearer its axis move slower than those which are further away. As you move north (or south) from the equator, you are moving closer to the axis of the Earth and so the air which started at the equator and moved north (or south) will be moving faster than the ground it is over (it has the rotation speed of the ground at the equator, not the ground which is is now over). This results in winds which always move from the west to the east in the mid latitudes.