Why would it be wandering around if it was stuck in a relatively small space? It can sit or lie down, being bipedal doesn't mean it needs to be constantly standing or walking.

I looked into this afterward and there's actually a study by Barrick and Showers (1999) estimating that a large tyrannosaur could consume 2 - 3 weeks' worth of food in a single meal, and that's before accounting for its existing fat reserves. Remember, a starving animal will burn through its fat reserves and eventually its muscle tissue before it dies, so at that size it's potentially got significant runway.

There's also Kleiber's law, which says larger animals have proportionally lower energy requirements relative to their body mass. Obviously a rex would need an enormous amount of food in absolute terms, but that doesn't mean it would actually need to eat particularly frequently. Throw that all together and i highly doubt a month would be enough to starve one to death.

Dehydration is a much better argument though, I'll give you that. I've no idea how long a rex could survive without water, and I doubt anyone can reliably estimate it. I'd imagine that would kill it long before starvation did.

Although interestingly, the original scenario only says you're provided with food, it doesn't actually mention water for either of you.

But if it rained, water would pool in its footprints and you'd definitely be screwed.