Seven years late!) but none of these answers gives a comprehensive explanation, particularly in that the OP's premise "westbound travel is slower" is only correct at certain latitudes.
This diagram shows the macro air circulation patterns around the globe. Generally, air is heated at the equator and rises, then travels at high altitude towards the poles. At about 30deg latitude the air mass has cooled sufficiently that it wants to descend, then heads at low altitudes back towards the equator. This is the Hadley cell. From space, these airflows appear largely Northly and Southerly. On Earth, the Coriolis effect makes the airflow also appear Easterly and the result is called the Trade Winds. Here, westbound air travel is faster than eastbound.
Similarly, air is cooled at the poles and descends, then travels at low altitude toward the equator to approximately 60deg latitude where warming makes the air rise. This is the Polar cell. The same low altitude direction toward the equator and the same Coriolis effect makes these wind directions match the Trades, and they are called the Easterlies.
Between the Polar and Hadley cells, wind in the Ferrel cell (30deg to 60deg latitude) blows toward the poles at low altitudes. With airflow reversed the Coriolis effect now makes the winds appear westerly, and are aptly called the Westerlies. This is where air travel in the US and Europe occurs, and this is where the OP's "westbound travel is slower" applies.
So both atmospheric heating/cooling and the Earth's rotation via the Coriolis effect determine the direction of the prevailing winds.