3. A certain number of boys and girls went camping during the summer break. They planned an ecological action that they would finish in 29 days if each child worked evenly - working the same part of the job in any given days. The boys worked a bit faster; in the same time, 2 boys do as much work as 3 girls. Fortunately, after three days of starting the work, a larger group of children joined them: boys - 8 times more than the initial number of girls, and girls - 18 times more than the initial number of boys. The newly arrived children worked with the same dynamics as the initially arrived ones. How many days in total were working days?
Solution. Let's assume that at the beginning there were $a$ boys and $b$ girls. Daily they complete $\frac{1}{29}$ of the work. Therefore, in the first three days, $\frac{3}{29}$ of the work is completed. Since boys work 1.5 times faster, the situation is the same as if these $a$ boys were replaced by $1.5 a$ girls, i.e., a total of $1.5 a + b$ girls. Thus, each girl completes $\frac{1}{29(1.5 a + b)}$ of the work daily.

Then, an additional $8 b$ boys arrive, which is equivalent to $1.5 \cdot 8 b = 12 b$ girls and $18 a$ girls. Now, all the children together complete the work as if there were $1.5 a + b + 12 b + 18 a = 19.5 a + 13 b = 13(1.5 a + b)$ girls. Therefore, if after the first three days it takes $x$ more days to complete the project, we get $\frac{3}{29} + \frac{13(1.5 a + b)}{29(1.5 a + b)} x = 1$, from which we obtain $3 + 13 x = 29$, i.e., $x = 2$. According to this, the entire project lasted $3 + 2 = 5$ days.