## 22. General Cleaning

A solid joint-stock company occupies three floors in a tower, which has the shape of a parallelepiped and is located in Paris in the La Défense district: the 13th and 14th floors, where the company's offices are located, and the 25th floor, where its board of directors is situated.

To clean these premises, a cleaning crew is called in, who work for four hours in the offices. Then the crew splits into two parts: half goes to clean the 25th floor, while the other half continues to clean the 13th and 14th floors. After another four hours, the crew stops working: the two lower floors are already completely cleaned, while the 25th floor is scheduled to receive another cleaner the next day, who will complete the work in 8 hours.

Assuming that the time required for cleaning is proportional only to the area of the cleaned premises, how many cleaners were in the crew called by the company?
22. Let $n$ be the unknown number of cleaners. The number of man-hours required to clean two floors of the bureau is

$$
4 \cdot(n+n / 2)
$$

The number of man-hours required to clean the 25th floor is

$$
4 \cdot(n / 2)+8
$$

But this last number is half of the previous one, since the area of one floor is half the area of the other two. Therefore,

$$
4(n+n / 2)=2(4 n / 2+8)
$$

From this, $n=8$, i.e., there were eight cleaners in the team.