Training for sprints and distance running

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I have my first 10k I'm training for that's in early august. The hope is to steadily increase my running distances each week until I get to 7 miles and then work on running 6 faster. Right now I am on 5 miles.

My problem is that it's also track season and I am looking to improve on my sprint times. I run the 100 and 200. Fortunately this ends 2 weeks before the 10k.

I am finding it extremely difficult to train correctly for both the sprints and the 10k. I would love to commit 3 days to running distance, but I also want to get 2 sprint practices in too (per week). Working out either group on consecutive days though seems to be yielding not the greatest results.

Does anyone have any advice or related personal experience they can share?