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
The bread and butter of the Rex is their high Health. A good way to find a high Hp Rex and know it's Hp stat before KO is to ride a mount and use the magnifying glass to see it's health. Griffins, Sabers, and direwolfves are all good mounts to ride while trying to use the magnifying glass on the Rex. Between 7000 and 10000 is what you want to aim for to make it worth taming.
NEVER IN ALL YOUR DAYS fight an alpha rex while a weaker dino is parked elswhere. It will get attacked by something else or the rex will lose interest in you and eat it. I lost a good level quetzal that way. Me and my thyla got revenge but that won’t replace the hours of searching and grinding out darts.