Certainly a week, probably longer. I have a packed “get home bag”, along sleeping bag, tent, first aid kit, along with other survival gear, including water purification. Food is limited to a few MRE packs, some sardines, crackers and energy bars, but I don’t think I’d run out of food for at least a week. And then I could probably last another few weeks just on body fat. I can make all the water I need with my purification gear, so water isn’t a concern.
I’d say up to a month, honestly. Wouldn’t be pleasant, but it’d be a lot more pleasant than dying.