Laws and regulations related to labor time of this country tend to be designed around the concept that you must have as much free time as the time you work and where possible this cycle must alternate. Being a week the measure of labor schedule, the most common implementation is alternate a week of work with a week free.
Jobs like some medical disciplines have a different schedule, but usually the principle mentioned above is honored in a way or another. Another example: miners mining in a location far away from cities, need to be hired full-time by a very long period of time, the breaks they need to take during that period, to maintain their good health, are still considered job time. Then the company/employer needs to compensate them in some way that complies with the mentioned principle.
If a company/employer doesn't honor this principle, it will sooner or later call the authorities attention. If a company/employer needs, or just wants, to employ people without honoring this principle, legal ways exist, but they need to have some very well crafted excuse as they will have to answer some questions. Many companies got the required permissions at first, but then, after some time, they were asked to go back to a "normal" schedule.
No need to say, but companies need, probably, twice as people as they would need in real life, to function the same time.
Another hard to solve problem, is that in real life many jobs pay per hours worked, and absences, specially unjustified absences, mean a lower income for the employer. So, our fantasy country's citizens need a very good wage, that allows them to survive that free week without reaching dangerous stress levels (I'm aiming for happy citizens), or either for the free week to be payed but this plays again the viability of the business.
Psychological aspects: like "if people feel like their physical and mental health allow them to do more work, they may want to work more and increase incomes". Making this system a bit difficult to justify. This may be a topic for another question.
Update: sorry, I used week of rest in place of week of free time. I noticed that "rest" sound like the citizen spend all the time sleeping while I actually refer to have free time.