This page of the Mr. Prepper guide contains information about the day and night system in the game, energy regeneration and the consequences of not going to sleep before 3 a.m.
A day in Mr. Prepper starts at 6 a.m. and ends at 3 a.m. You can go to bed at 8 p.m. already.
While you sleep, the time skips to 6 a.m. Your energy is recovered (depending on the length of sleep), your health / hunger level decreases and the Preparedness level slightly increases. In Mr. Prepper, sleep is the only option to save the game.
Of course, the morning marks the next calendar day. It is worth checking the wall calendar to know in advance what awaits you on the next day. You should pay attention to things like water/power cuts, lack of a postman, and agent's inspections.
What are the consequences of insufficient sleep? If you don't get to bed before 3 a.m., your character will faint for a random amount of time. When you wake up, you will appear at the start of the location where you fainted.
Using the T key, you can open the time bar. Use it to decide how much time you want to skip. The second way that you will need most during exploration, when the hero moves from one place to another, is fast-forwarding.
Hold Left Control to speed up the time twice. Hold the key as long as you wish. To stop time skipping, press the P key to pause the game.
Fainting takes the most of your time. It may take a few hours or even a few days.