# Task 4.

Four brigades were developing an open coal deposit for three years, working with a constant productivity for each brigade. In the second year, due to weather conditions, work was not carried out for four months, and for the rest of the time, the brigades worked in rotation (one at a time). The ratio of the working times of the first, second, third, and fourth brigades and the amount of coal mined respectively are: in the first year 4:1:2:5 and 10 million tons; in the second year $2: 3: 2: 1$ and 7 million tons; in the third year 5:2:1:4 and 14 million tons. How much coal would these four brigades have mined in 4 months if they worked together?
Solution. Let the $i$-th brigade mine $x_{i}$ coal per month. Then we have the system

$$
\left\{\begin{array}{l}
4 x_{1}+x_{2}+2 x_{3}+5 x_{4}=10 \\
2 x_{1}+3 x_{2}+2 x_{3}+x_{4}=7 \\
5 x_{1}+2 x_{2}+x_{3}+4 x_{4}=14
\end{array}\right.
$$

By adding twice the first equation to thrice the second and subtracting the third equation, we get

$$
9\left(x_{1}+x_{2}+x_{3}+x_{4}\right)=27 \text {. }
$$

Then

$$
4\left(x_{1}+x_{2}+x_{3}+x_{4}\right)=12 \text {. }
$$

Answer: 12 million tons.