You don't have to be faster then the Rex just faster then your tribe mate.

If your low level. RUN FOR YOUR LIFE!
P.S. If your high level still run

Always have a bola at the ready, although you may not be able to bola the Rex, you can still bola your tribemates to escape.

Carea more about big prey than you, so try to run past anything bigger and meatier than you, then keep running. It won't take long to kill whatever it finds. That being said, I did see a Rex take a long while to kill 2 carbonenemy turtles