Now you find food and... you don't eat it. You sleep on it?
Of course you eat it ... -_-
Come on, this is just matter of "stopped day time" in this game ... same as we are able to run around the map for 8 hours of real time, while there is high Noon this whole time in game ... and then, when we press long rest button to "end the day" all that time magicaly pass, and we have midnight ...
The same mechanic is used for food ... our characters are obviously eating and drinking whole day ... and when the day is ended, and we "wrap it all up" ... our amount of food supply is reduced by what we roleplay-wise "have eaten during that day". :-/
Seems like quite easy concept to me ...
Havent you never done anything simmilar in Tabletop sesion? O_o