You want to sprint on the same day as your weights in order to let the CNS have a day to recover. Sprint first; then you have 2 options, strength train directly after your speed sessions or as creed said, wait around 4-5 hours after speed work.
If you train directly after, you may notice a slight dropoff in strength level (not much at all though), however you will have more recovery times b/w speed sessions.
If you train 4 or so hours after speed than you will probably be a little more efficient in the weight room but will have less recovery time before the next speed session.
I use a combination of both methods depending on how much time throughout the day I have to sprint and strength train.
Make sure you are sprinting at 95% or above, any less and you are wasting your time unless you are doing tempo runs and if so, then you should do them at about 70% or lower so that you don’t fatigue the CNS. Do your tempo runs on T, TH, Sat. or basically on your off days. Take Sunday off. The tempo runs help with recovery and can shed some extra bodyfat if that is an issue.
Go to Charliefrancis.com for more info on sprinting such as volume,intensity, etc.
Now, Go Run!