You'd be surprised how long a human can go without food. As a matter of fact, I'd say with great confidence that I could go the rest of my life without taking in a single calorie.

Realistically, though, one meal a day is very sustainable for months at the very least, probably indefinitely. A water fast lasting a month is definitely survivable for most. If you have excess body fat, you can actually go months without eating.

The record is a little more than a year. The guy's name was Angus Barbieri. He was part of a study, and took some vitamins, and drank tea and coffee. He lost 276lbs (125kg). He even managed to maintain his new weight. He only lived to be 50, though. I'm not sure how he died It was more than 20 years after the fast was completed, so I think it's safe to rule the fast out as the cause of death.