a fight from east to west, (e.g. Australia melbourne to perth) takes longer than travel backwards. (west to east).
What's the reason?
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The speed of an aircraft during the flight is ideally kept constant relatively to the air surrounding the aircraft. However, in the moderate zone - between 30 and 60 degrees of latitude on both hemispheres - the dominant winds are called westerlies
for a good reason. They blow from the West to the East. So it's faster to get from Perth to Melbourne because it's in the direction of the wind; but it takes a longer time to fly from Melbourne to Perth because it's against the wind and, again, the natural speed of the aircraft is measured relatively to the air (i.e. wind).
Why do the westerlies have this direction?
It's because of the Coriolis force. The Coriolis force - a "fictitious" force in a rotating frame that adds to the centrifugal one - steers winds (and rivers) in the clockwise direction on the Northern Hemisphere and counter-clockwise direction on the Southern hefmisphere.
Why does the Coriolis force create westerlies - which are particularly strong on the Souther Hemisphere e.g. in Australia? It's because the normal air that heats up near the equator expands and it would travel to one of the poles. However, this air going towards the poles gets steered by the Coriolis force, so before it reaches e.g. the Southern pole, it's already moving in the East direction.
The westerlies are weaker on the Northern Hemisphere as well as on the summer-having hemisphere because when it's so, the wind from the equator is strong enough (amplified by the land on the Northern Hemisphere, or by the summer) so that it usually manages to reach the pole (without drifting to the East), anyway.
It's very, very far but my uncle lives in Melbourne while a generous IT expert who lives in Perth sent me an iPod Touch for a relatively modest and doable help with a project half a year ago. ;-)