How to transition from Base mileage to race training?

Ask your coach what he think you should do.

Talch wrote:

Ask your coach what he think you should do.

I don't have a coach, nor do I think one is necessary.

If you haven't been doing any kind of speed/faster running, rather than jumping into a full speed workout you might consider starting with a lower stress fartlek workout: Either 100m/100m or 200m/200m fartlek could be a good introduction. Basically alternate a 200m at 5k pace with 200m easy running (say around 55 seconds). Continue for up to 25 laps (10k) of continuous running. (This was an idea from one of the Hadd threads).

Another good idea for transitioning base->speed is the Lydiard hill circuits, but if you only have 3 weeks that's probably not enough time.

Hit the hills.

Something that might serve you well both as preparation for this 3k and for the rest of your season as a whole is short, faster than race pace intervals with long recovery. These aren't the same type of workouts you'll do when you're really trying to get race fit and then peak, but they do get you used to running fast while staying relaxed and also serve as a transition to the harder workouts (long VO2 max intervals, shorter fast intervals with short recovery) that get you in or near PR shape and peak fitness later in the season.

Something like 2x6-8x200 @ mile pace w/ 200 SLOW jog recovery and 800 SLOW jog set break would be a workout that fits this description. After a few weeks of these you'll be ready for the 5-6x1000@ 3k pace w/ 2:30 recovery and 10-12x400 @ mile pace w/ 60s recovery ball-busting type workouts.