I want to run faster!

I like to run fast. I like to win stuff, conquer stuff, be awesome, all of that. I'm not there yet, and I know that. But I will get there!
My body really wants to run at a 6:15-7:15 pace (this is per mile), but I can't maintain it right now. Legs, I promise to raise my fitness level, and one day you can move at your preferred rate!

Really though, right now I'm doing most of my long runs at roughly a 10 minute pace, sometimes a bit faster. My two fastest runs have been just under 9 minute pace, 8:52-8:54 per mile, average.

This is what I've been doing the past couple weeks, at my current fitness level, not necessarily in this order. I am trying to learn to listen to my body (and reading Runner's World), so I adjust workouts accordingly. It's been a long time, so my listening skills are definitely in the working-on-it stage, but we're doing pretty well.
2 days of long slow runs at ~10 minute pace, ~3.5 miles
1 day speed work - typically some form of fartleks or tempo runs
1 day faster pace, this is where I just broke 9 minute pace, 3 miles
1 day slightly slower, something like 9:20ish, 3.5 miles

Today I did fartleks. Always exhausting! Today when I started them, I said, body, go! And my body went...at a 6:18 pace. In fact, my first 4 fartleks were all 6:40 pace and under. This is much faster than I can go for more than a minute at a time right now, but I want to work up to this pace for longer amounts of time.

When I got back to running a few months ago, I was having trouble maintaining a 10:30-11:00 pace for more than, say, a mile. Already I have improved so much, and I am really excited! Guys, this is so cool!