13.135. A team of mechanics can complete a certain task of processing parts 15 hours faster than a team of apprentices. If the team of apprentices works for 18 hours on this task, and then the team of mechanics continues working on the task for 6 hours, only 0.6 of the entire task will be completed. How much time does the team of apprentices need to complete this task independently?
## Solution.

Let $x$ hours be necessary for the students to complete the task; $x-15$ hours for the team of mechanics. In 18 hours, the students will complete $\frac{1}{x} \cdot 18$ of the entire task, and in 6 hours, the mechanics will complete $\frac{6}{x-15}$ of the entire task. According to the condition, $\frac{18}{x}+\frac{6}{x-15}=0.6$, from which $x=45$ hours.

Answer: 45 hours.