Quick question

Alright, so I've been training for some half marathons lately. I can currently run them in about 1hr 25mins. But for a team that I'm trying to join thats pretty popular in my area, I need a ton of upper body strength. My running schedule usually has me doing a 8-10 miles six days a week. I plan to run to my gym, work out, then run back home. That'll most likely be around ten miles there and back. Would it be better to do that, or just run ten miles, then drive to the gym?

 

do ten miles, then drive to the gym..
im not an expert, but i think your muscles would be overworked if you did an intense workout then ran 5 miles home..
i'd play it safe