Here's a little tip I learned which is I think starting to make me a little faster, plus it strengthens my legs....

On my older bike, the Shimano hubs are almost silent when I coast along without pedaling, so whether or not I am pedaling my bike is pretty quiet.
On my new bike, when i coast the hubs make a clicking/buzzing noise. At first I didn't like it much, but then I got used to it and thought it reminded me of crickets, kind of a strangely satisfying sound. But then the crickets made me more aware of just how often I was coasting without pedaling. It was often. So now I play a little game with myself and try to keep the "crickets" quiet by pedaling as much as I can as opposed to automatically coasting whenever I can.

So, if you want to increase your average speed, try to avoid coasting.