Task 4. The segment $AB$ with point $S$ is divided into two parts which differ by $8 \mathrm{~cm}$. Find the length of the segment if the shorter part is one-third the length of the longer part.
Solution. Let $x$ and $y$ be the lengths of the segments into which the line segment is divided. From the condition of the problem, the lengths of the divided segments are $x$ and $x+8$ (in other words, $y=x+8$). But, again from the condition of the problem, $x+8=3x$. Then $2x=8$, so $x=8:2=4 \text{ cm}$.

A $S$ B

Thus, the lengths of the divided segments are $4 \text{ cm}$ and $12 \text{ cm}$, and the total length of the line segment is $4 \text{ cm} + 12 \text{ cm} = 16 \text{ cm}$.