I'm 57 and started about 3 years ago after nearly 40 years off. Some of the old habits remained. I started on a flat bar hybrid and was much more comfortable when I got back on vintage steel with downtube shifters. It just felt right.

Within about 6 months, I was averaging around 14 mph riding anywhere from 20 to 50 miles. Didn't really get much faster after that. I can do 15 mph if I just concentrate. Your mind tends to wander and you slow down a bit if you don't maintain a bit of focus. If I really work, I can get to 16 mph, but can't hold that for more than about 25 miles. And only achieved that recently as I sort of figured out how to attack our modest hills with a bit more effort. (Average routes are 300 - 400 ft/10 miles.)

I do virtually all my riding alone. You get faster if you ride with faster riders. Or if you train harder than I care to. I calculate my speed by getting distance off ride with GPS and dividing by clock time from when I walk out the door to when I get back in. I never got a computer because I didn't want to obsess too much while riding. Although I obviously still worry about it enough to keep track.

(edit - I ride alone or with my wife. She has a computer and on those rides we're booking if we hit a 12 mph average. But I enjoy those rides just as much.)