If you don’t hook up with a coach - and I recommend you do - you will need an accomplished partner to hold you to your workouts, or a great deal of self-discipline. For the workouts, there will be a combination of strength, endurance, and speed drills that will get you where you want to go. Simply put, stronger muscles, that can perform longer, will increase your time in the air by reducing your ground contact time. You will literally fly toward your goals!
Things like leg presses, squats, lunges, etc. will build up the strength of the muscles. Endurance will come from things like hill repeats, and when you are ready to put it all together, those sprint times should start coming down.