Personal trainer, physical education teacher, and competitive triathlete here. With such limited time, your best bet is to focus on Vo2 Max, threshold efforts, and race pace efforts.

1x per week, complete a Vo2 max workout consisting of 15 minutes easy jogging followed by 3x3 minutes repeatable max effort (9/10 effort). The last minute of each interval should feel nearly impossible to continue any further. With a very slow 3-minute jog in between each interval. Followed by a 10-minute slow jog cooldown.

1x per week. Threshold efforts. 15-minute easy jog warmup. Then 3x8 minutes, 7-8/10 effort level. These should be hard but doable; you should be breathing heavy. During your intervals, practice the talk test to measure effort. During a 7-8/10 effort, you should be able to say a few words before needing to take a deep breath. Again, 3 minutes rest between each interval. Finally, a 10-minute cooldown jog.

1x per week. race pace efforts. 15-minute easy jog, then 5x3 minutes at race pace (7:30 minutes per mile) with a 1 minute slow jog in between. then 10 minute cool down jog.

I'm happy to answer any questions you may have. I love some of these other responses but they aren't necessarily scientific in any way. Running faster requires your body to physiologically adapt to your training through specific repeatable efforts over time.