I would prefer to have them just use it as Camp Rations per Long Rest like you do in a tabletop. When you run out people can start making con Checks to see if you start to get Starvation status effects as per 5e Ruleset. There are spells and backgrounds that can help obtain some ( Like Outlander ) but that would be the choice the player can make on their own
This would then put a finite timer on the amount of long rests one could actually do in Act 1.
