I don't seam to be getting faster as I age I do keep my cadence up 75-83 most of my rides but my mph is only about 10.5 avg, some days I catch myself dwadling and lose all track of speed and cadence, I am just enjoying where I am in time and space. or it could be that old age thing, 67.
I use to race but that was 30 years ago! If you want your speed to increase you need to study the internet and find out how to that, such as interval training. Interval training will make you a better faster rider and there are web sites you can find to get that info, just search by asking:
bicycle interval training workouts and study the sites then put the stuff into practice. Also join a local riding club, riding with others forces you to ride faster and most clubs have senior members, and it's a great place to meet people that share your hobby.
Don't let your age fool you, most older people lie to themselves saying they can't do this or that due to age, it becomes a self fulfilling prophecy!! If you practice the interval training routine your speed will increase if you do this stuff, I guarantee it! You won't become a Lance Armstrong obviously, but you could, if you wanted to, compete in racing events against other seniors, maybe you won't win any races but your speed will increase and you'll have fun doing it.