Maximum strength and maximum possible long-distance speed are incompatible. However, unless you are hoping to win a half-marathon, the maximum possible speed may not be an issue. A respectable time may be more important depending on what you want in which case you may wish to work out in a gym to increase the strength and size of all you muscles even if that slightly reduces your speed.
Increasing muscle mass means increasing body weight and that is not desirable for maximum possible long-distance speed, but would not be a problem for sprinting unless carried to extremes. It could be helpful to do leg exercises in the gym but instead of trying to gain maximum strength, limit the weight, keep the repetitions high, and do the exercises fast. The first runner to break the 4-minute mile could barely do pushups.
It would be helpful to have a timed interval workout once per week, preferable on a track to expedite timing; I used to do intervals on a track. After warming up by running a mile at about an 8-minute pace (which was very easy for me), I ran 3 quarter mile intervals jogging a quarter mile after each one to recover. I ran all three at the same speed with the speed selected so that I could barely run the last quarter mile interval at the same speed as the first two. I always used a stop watch.
After the quarter mile intervals, I ran 3 one-eighth mile intervals in a similar manner, jogging a quarter mile after each to recover. Then, I ran three 100 yard dashes at the maximum possible speed, jogging a quarter mile after each. Following that, I again ran a mile at about an 8-minute pace, then walked about a quarter mile. Interval workouts will increase the speed that you can maintain for long distances but doing them more than once a week may not be a good idea since it would increase the risk of over-use injuries.
There are other ways to do intervals, but that worked for me and increased the speed I was able to maintain for 10 miles. In fact, when I was 50, I was able to run 10 miles in less than 70 minutes, i.e., a pace of less than seven minutes per mile.
In addition to the weekly interval work out, I'd suggest two additional runs per week, but not on consecutive days. You can do the gym work-outs on days you are not running.
I believe in experimenting. What works for one guy doesn't necessarily work for other guys.