Note: No plagiarism intended.
My deep apologies of some of the scheduling goes against anything cannon in TOS. To be honest, I simply made this up to explain things I have said in previous chapters. I hope it makes well enough sense.
Chapter 4:
Let's take this time to explain the schedule on the USS Enterprise. Crew members work on shifts in an alternating work, break, work, sleep pattern. The times for when these shifts start are categorized into 6 staggered groups, so that the whole crew is never on break at the same time. The groups are group A, B, C, D E, and F. No matter what group you are in, the shifts are always the same length. Six hours of work, 4 hours of break, 6 more hours of work, and 8 hours of sleep. Here is group A's schedule:
4:30-10:30 Working shift
10:30-2:30 Recreational Break
2:30-8:30 Working shift
8:30-4:30 Sleep
The next group, B, follows the same pattern only one hour later. The same goes for C, D, and E. Group F, unfortunate as they are, have their schedules flipped; their working shifts occur while most everyone else is sleeping.
McCoy is a group A, and Chekov a group B. Quite fortunate for them that their schedules line up so well, so they get most of their break time together.
In case you wanted to know, Jim is an A, Spock and Sulu are B's, and Scotty and Uhura are C's.
The schedule may seem a bit extreme, but everyone on the Enterprise is fully accustomed to it and follows it obediently.