You will go faster *for the same effort* on a lighter bike, especially where climbing is concerned. That is because speed depends on your power to mass ratio. Mass is the weight of you and the bike, so if that is reduced, especially rotational weight (wheels, hubs, etc.) you will be faster. But as Veronica said getting to 18-20 mph requires mucho series training and a super light bike both. But getting from 12-15 mph to 14-17 is realistic with consistent riding and a lighter bike (average speed too depends a lot on how hilly it is where you ride).