13.288. A master and his apprentice were tasked with manufacturing a batch of identical parts. After the master worked for 7 hours and the apprentice for 4 hours, it turned out that they had completed $5 / 9$ of the entire work. After working together for another 4 hours, they found that $1 / 18$ of the entire work remained to be done. How long would it take the apprentice to complete the entire work on his own?
Solution.

Let's take the entire volume of work as 1. Let $x, y$ be the labor productivity of the master and the apprentice per hour, respectively. According to the conditions, we have the system

$$
\left\{\begin{array}{l}
7 x+4 y=\frac{5}{9} \\
7 x+4 y+4(x+y)=1-\frac{1}{18}
\end{array}\right.
$$

The time required for the apprentice to complete the entire work is $-\frac{1}{y}=24$ (hours).

Answer: 24 hours.