I'm currently training for my first 10k (the race is in a month and am in a good position from a training perspective). With where I'm at training wise, I'm starting to look ahead to the next goal for me. I'm looking at doing a half marathon next year but am wondering about how I should go about this.
Currently, my pace for running is around 13:00-13:30 a mile. Yes, I'm that slow. Because of that, I'm wondering if I should spend some time on speed before starting a training program for the half. I have plenty of time before any half I'd do (it wouldn't be until next spring) and I'm wondering if speeding up my pace would have benefits. I know training for the 10k, I used one of the couch to 10k apps which are all time based (they get you to run for an hour), but that left me short of being able to actually finish a 10k (I finished my program a couple weeks ago and am working on the gap between the hour and how long it will take me to finish). As I go for longer distances that gap will only grow.
So my question is, does it make sense for me to spend a couple months working on speed before diving into a half marathon training program or is there not a lot of benefit and I should just go into the next program?