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. Both the prevailing winds and the jet stream affect duration of air travel, and both depend on differential heating and the rotation of the Earth.

**Prevailing Winds**

[This diagram][1] 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 Northerly 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.

[![enter image description here][2]][2]

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.

Polar and Hadley are driven by polar cold and equatorial heat. If the Earth were smaller they would combine into one cell. At the existing scale an intermediate cell forms, the Ferrel cell, and its direction is driven by contact with Polar and Hadley at 30deg and 60deg. 

Polar makes a "chimney" at 60deg which is shown on the chart as low pressure. Hadley makes a downdraft at 30deg, shown as high pressure. The Ferrel air mass flows from high pressure to low, or toward the poles at low altitude. 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, and consequently the amount of time air travel takes in a particular direction.

**Jet Stream**

This phenomena occurs in addition to the prevailing winds and is affected by the same factors. There are usually four jet streams, one located near each of the vertical air flows between the circulation cells. The 60deg latitude Polar jet streams are stronger and lower than the 30deg Subtropical streams, and this explanation focuses on the northern Polar jet.

From [this diagram][3] you can see circulation in the norther Polar Jet. Looking Eastward in the direction of the jet stream airflow there is a counter-clockwise rotation between the Ferrel and Polar cells. Though this entire column of air is ascending, the temperature differential between the colder air of the Polar cell and the warmer Ferrel air causes this weak rotation. Location and altitude fluctuate, but the lower reaches are around 30-40kft where transport aircraft fly.

[![enter image description here][4]][4]

You might think that the lower altitude flow toward the equator would combine with the Coriolis effect to create a mild easterly flow as happens in the Polar easterlies. It does attempt this but runs into the much stronger Westerlies and is deflected, accelerating as it moves in a westerly direction. Think wind blowing into a wall, deflected to move along its length. Depending on local temperatures, the deflected air can reach speeds as high as 200kt.

  [1]: https://thegrandmalogbook.blogspot.com/2019/08/trade-winds-vientos-alisios-in-canary.html
  [2]: https://i.sstatic.net/ViWmS.jpg
  [3]: https://www.code7700.com/weather_tropopause.htm
  [4]: https://i.sstatic.net/pSQI1.png