Can I do weight cross training followed by long distance running on the same day?

I have a cross training program that involves some weight. But mostly push-ups, pull-ups, and curls (bicep, tricep) and shoulder presses.

Can I perform these cross-training weight workout (about an hour long) then do a distance run (starting at 1 mile, then increasing by .5 miles a week until I’m doing 4-5 miles).

If you care, the cross training weight workouts are the P90X workouts (I love them).

My main reason to do this is to prepare for Cross Country while KEEPING (NOT BUILDING) my muscles.

Thanks.