Under certain conditions, riding a fixie (defined as a fixed-gear bicycle, rather than single speed) can be more efficient than a geared bike and therefore faster over a given course. Here's why:
1. The chainline on a fixie is more efficient, so less resistance to pedaling forces. No slanted chain angle, no jockey pulleys to move. Indeed, the first derailleur systems devised tried as much as possible to maintain the direct chain run to the cog just because it was more efficient.
2. You don't have to pedal over top dead center on a fixie; the rear cog does that for you. TDC is the "dead" spot in the pedal revolution. Getting your pedal over tdc 90 times per minute for each crank on a one-hour ride can be relatively more taxing.
3. Up to a certain grade, a fixie can actually be faster than a geared bike on a climb just because it happens to be geared more optimally for that grade. As long as the route doesn't exceed that optimal grade for the fixie's gear, the fixie could be faster because on a geared bike, you could be shifting down to a suboptimal gear for that grade.
4. The temptation for most riders is to overgear. This causes the bike to "bog down," but most riders will refuse to admit this. Bogging down leads to lower speeds and an earlier onset of tiredness. On my fixie, I still feel fresh at 100 miles just because I haven't been able to gear up. I don't feel as fresh on a geared bike, but then I might have got to 100 miles faster because I was in a bigger gear and not bogging down, but pushing it, rather than spinning it.
5. And a very minor point: on a fixie, you're not carrying two useless derailleurs and an 11-speed cog, plus extra shifters.
Luis