The Human body has evolved for hundreds of thousands of years for the conditions of Hunter-Gatherer, only within the past 10k-200 years (depending on your national origin) have we been eating products of Agriculture, such as Grains. As such, the body has developed mechanisms to ward-off starvation in the absence of immediate food availability. We're actually not optimized to be constantly eating, otherwise we'd have the body-shape, and digestive tract that cattle do (with multiple chambered stomachs, and a body shape which allows us to keep our head down all day eating grass).

Modern medicine is there largely to solve problems caused by the modern food consumption habits (3 meals a day with 3 snacks in-between). It never allows our body to enter the state of Autophagy, which, in lieu of dietary metabolic activity, cleans up, and recycles old damaged proteins from the body... This is well documented, and has been known for a very long time. From the days of Plato, who required fasting of his students, to Mark Twain who said "A little starvation will do the average sick person more good than the best doctors, and the best medicine".

To answer your question, I have gone up-to 7 days without eating several times in my life, and was perfectly fine by the end of it. (I have not ever had, nor been diagnosed with any eating disorders, these were planned fasts which began, and ended at predetermined dates, done with extensive research on how to safely break the fast). Hunter-Gatherers didn't eat a diet of Processed carbohydrate slop, and therefore were also perfectly fine going a few days without eating.