13.021. One brigade can harvest the entire field in 12 days. The second brigade needs $75\%$ of this time to complete the same work. After the first brigade worked alone for 5 days, the second brigade joined, and together they finished the work. How many days did the brigades work together?
## Solution.

Let the teams work together for $x$ days. The productivity of the first team is $-\frac{1}{12}$; the productivity of the second team is $-\frac{1}{12 \cdot 0.75}=\frac{1}{9}$. According to the condition, $\frac{1}{12} \cdot 5+\left(\frac{1}{12}+\frac{1}{9}\right) \cdot x=1$, from which $x=3$ days.

Answer: 3 days.