Problem 4. In an album, a grid rectangle $3 \times 7$ is drawn. Robot Igor was asked to trace all the lines with a marker, and it took him 26 minutes (the robot draws lines at a constant speed). How many minutes will it take him to trace all the lines of a grid square $5 \times 5 ?$
Answer: 30 minutes.

Solution. Note that the grid rectangle $3 \times 7$ consists of four horizontal lines of length 7 and eight vertical lines of length 3. Then the total length of all lines is $4 \cdot 7 + 8 \cdot 3 = 52$. It turns out that Igor spends $26 : 52 = \frac{1}{2}$ minutes on the side of one cell.

The rectangle $5 \times 5$ consists of six vertical and six horizontal lines of length 5. Thus, the total length of the lines is $6 \cdot 5 + 6 \cdot 5 = 60$. Then it will take Igor $60 \cdot \frac{1}{2} = 30$ minutes to outline it.