Problem 2. A segment with a length of 89.6 cm is divided into four parts such that $\frac{1}{2}$ of the first part is equal to $\frac{1}{3}$ of the second part, $\frac{1}{3}$ of the second part is equal to $\frac{1}{4}$ of the third part, and $\frac{1}{4}$ of the third part is equal to $\frac{1}{5}$ of the fourth part. What is the length in centimeters of each of these parts?
Solution. Let $x_{1}, x_{2}, x_{3}, x_{4}$ be the first, second, third, and fourth part, respectively. Then

$$
\frac{1}{2} x_{1}=\frac{1}{3} x_{2}=\frac{1}{4} x_{3}=\frac{1}{5} x_{4}=k
$$

that is,

$$
x_{1}=2 k, x_{2}=3 k, x_{3}=4 k, x_{4}=5 k
$$

According to this,

$$
2 k+3 k+4 k+5 k=89.6
$$

from which $k=6.4$. Therefore, the parts are $12.8 \mathrm{~cm}, 19.2 \mathrm{~cm}, 25.6 \mathrm{~cm}$ and $32 \mathrm{~cm}$.