Like others already said: 20 mph is a little fast for an average speed.
If you don't apply the brakes and the terrain is perfectly flat you could do 20 mph average speed. But even then, after the 30 minutes it would take you to finish your commute you would be quite tired.
I have a 4.5 miles commute one way.
Almost all on bike trails, almost all flat.
Three stoplights.
It takes me 35-40 minutes from when I exit my apartment until I enter my office.
If I would give it all I have I think I could do it in 25 minutes, but it would be a little unsafe as the route goes through a parking lot and I have to pay attention to cars entering/exiting.
Plus I have to be able to wear my normal clothes, else changing clothes would mean more time or the commute
So I would say plan for 45 minutes for your one way commute.
The best way to estimate is to try the route on a Saturday/Sunday and see how it feels.
Good luck, I enjoy riding my bike to work.
Especially since it is my first time riding a bicycle in the last 14 years :).
I have around 500 kilometers (330 miles) in 3 months.
I am curious if I will still do it when the rain comes - I will have to buy fenders and some clothing I think.
Just a thing to look at:
http://www.bicycling.com/training/2015-tour-de-france/you-versus-tour-de-france-pro