I am a surgical resident who is sometimes scheduled to be on call in the hospital on Shabbat. Since I live a good 45 minute walk from the hospital, and just outside of the eruv, I don’t have food on Shabbat. Occasionally, I either don’t have the material or the time to make Havdalah in the hospital on Motzei Shabbat and do not have time to leave the hospital until Sunday night. Is there any way I can drink or eat before making a belated Havadalah to avoid fasting for 2 days?

Havdala takes no more time than a cup of coffee. You should make sure that during the week you bring a bottle of grape juice or beer to the hospital, some cinammon or other fragrant spice and two candles. Using them on Motzei Shabbat should not present a difficulty since the time needed is no greater than that needed to eat, drink, or go the bathroom. I would recommend that during the week you leave a couple of cans of tuna or other canned food in a locker for Shabbat together with a box of Matzot. If you continue to have difficulties it must assume it is for other reasons- discrimination? no suitable place to make a bracha?- and not just time constraints.