The famous phrase taken literally could turn into an actual game. The aim of such competition would be to prolong your day (the time that the sun stays above the horizon) by traveling west. Imagine few groups of people with equal (or different) financial resources, who all start in the same (or different) geographical location(s) with the goal to get as far and as quick west as they can.
It might seem simple at first - just find the flight that's going the farthest in that direction, but in reality, the outcome would depend on many factors (the location you start from, finances you have, availability of transportation in a certain location, cooperation of the team, etc.) and would require pretty much of strategic planning. Planes would definitely be used the most, but other means of transport also (both to get to the airports and in some cases with lack of better possibilities - to prolong the day). For example, you could prolong the day by some 20 minutes by driving a car west for a few hours and this might be very useful in some situations.
The competition could last just one day (until all groups experienced sunset) and then the daylight hours of each group be counted or it could last longer and daylight hours of different days could be summed up.
PS: It's also possible to prolong the day by traveling in a south or north direction (depending on the season of the year and the hemisphere) and to totally "hack" it by being above the arctic circle at the right time, where the sun doesn't set at all. But "hack" could be excluded by the rules, leaving the west (or south-west or north-west, depending on the circumstances) direction the most practical.