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No real way of knowing until you get out there. I rode fixed for two years solid and actually found my first few weeks i was slower with gears i guess due to the momentum that riding fixed brings, you should see a good improvement on hills however that is if you are using your gears correctly and spinning for the win, and feel fresher.
On a personal note i would average about 17.2 over a rolling route near me, when on gears my average is 18.5-19 solo but this is obviously very subjective to terrain. Head wind blah blah so i tend not to even worry about average speed as way to many things can factor in.
I'm just getting to the end of the build of my first road bike (Ritchey Road logic) having only ridden fixed with strava I would normally average between 16/17 MPH on a normal 50 ish mile route.
How much faster do you think I'll be with gears and a freewheel, all things being equal and working on the idea that gears are to make you faster rather than life easier. (if that makes sense)