The source of the “3 days” number likely comes from an experiment two scientists did in 1944 where they ate only dry food for a period of time; one ended the experiment at 3 days in, and the other at 4 days in. However since they stopped the experiment before being in any real danger, the actual survival time at room temperature likely exceeds 3-4 days.
The average person could probably still be saved after 5 days without water or more.
In the section about water:
The average person could probably still be saved after 5 days without water or more.