Problem 2. Two painters are painting a 15-meter corridor. Each of them moves from the beginning of the corridor to its end and starts painting at some point until the paint runs out. The first painter has red paint, which is enough to paint 9 meters of the corridor; the second has yellow paint, which is enough for 10 meters.

The first painter starts painting when he is two meters from the beginning of the corridor; and the second finishes painting when he is one meter from the end of the corridor. How many meters of the corridor are painted with exactly one layer?
Answer: 5 meters.

Solution. The first painter starts painting 2 meters from the beginning of the corridor and finishes at $2+9=11$ meters from the beginning of the corridor.

The second painter finishes painting 1 meter from the end of the corridor, which is 14 meters from the beginning of the corridor, and starts at $14-10=4$ meters from the beginning of the corridor (Fig. 1).

![](https://cdn.mathpix.com/cropped/2024_05_06_83a6c5e4a5c18bfc804cg-1.jpg?height=182&width=709&top_left_y=1304&top_left_x=370)

Fig. 1: to the solution of problem 2

Thus, there are two sections of the corridor that are painted with one layer:

- the section from 2 meters (from the beginning of the corridor) to 4 meters (from the beginning of the corridor) was painted only by the first painter (length of the section 2 meters);
- the section from 11 meters (from the beginning of the corridor) to 14 meters (from the beginning of the corridor) was painted only by the second painter (length of the section 3 meters).

This results in $3 \mathrm{m}+2 \mathrm{m}=5 \mathrm{m}$.

## Criteria

3 p. The correct answer is obtained.

4 6. The correct answer and justification are present.

The justification is considered to be a "picture" showing the sections painted by the painters.