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I have an old Bicycling magazine that has a graph showing power vs speed for a 10 speed bike. The name of the article was "What Effects Bicycle Speed?". If the author had used good grammer he would have used the word "Affects". The graph shows that you need about 0.16 HP to go 15 MPH and 0.25 HP to go 20 MPH. I think that 30 MPH required about 0.9 HP. A physically fit person can make 0.25 horsepower for several hours. One horsepower is about the limit a person can do for a quick burst of speed for 10 seconds or so. A one horsepower motor would really speed up hill climbing.
Lets say we have a hill with a grade of 10% and a bicycle and rider weighing 200 lb. The grade is the tangent of the hill angle (rise/run). The sine of the angle determines the force to be overcome by the motor and this is almost the same as the tangent for small grades so the force is about 200 lb * 10% = 20 lb.
V=375*P/F
so if F=20 lb. and P=1 HP
V=375*1/20
V=18.75 MPH
You could climb the hill at 18.75 MPH if there were no other drag forces.
If you had a gasoline engine with reasonable efficiency (0.5 lb/HP*Hr) connected to the bike using 0.25 HP and going 20 MPH on level ground, we can calculate the MPG.
MPG=D*V/(BSFC*P)
The density (D) of gasoline is around 6.25 lb./gal
MPG=6.25 LB/GAL * 20 MPH / (0.5 lb/HP*hr * 0.25 HP)
MPG=125/0.125
MPG=1000
So we can get 1000 MPG on a motorized bicycle if the speed is limited to 20 MPH and gear ratio and displacement are correct. A 12 cc engine running at 2500 RPM would be about right. Even better economy can be achieved with some aerodynamic improvements to the bike.
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