So I read a great article here, Competitor Online. It breaks down to this, without all the stuff you may not understand. If you want to run faster, train your feet, legs, and brain to do so. People I talk to all the time think that only fast people can get faster. Also, that once you get to a certain age, you cannot be fast anymore.
First, anyone can get faster. That doesn't mean you will be Olympic fast, but you can get faster. Also, when you do some of the things needed to achieve speed, the double secret bonus is that it helps with weight loss if you want to kick a few pounds. I am going to paste what I believe is the most important part of the article for you, the examples of the work needed. Basically, its training your feet and legs to fire faster. Feel free to read the whole article, it isn't long. Aim to do these drills a couple times a weak, just after warming up. The goal is for you to be totally fresh and do these drills with precision/accuracy. Enjoy!