Task B-1.1. (20 points) "Tomislav and I," said Krešimir, "can finish the job in 20 days." However, if I worked with Ivan, we would complete the job 5 days earlier."

"I have a better combination!" said Ivan. "If I worked with Tomislav, we would finish the job in one-fifth of the time it would take me to work with Krešimir."

How many days would each of them take to finish the job alone, and how many days would they take to finish the job working together?
Solution. Let $x, y, z$ be, in that order, the number of days it would take for Tomislav, Krešimir, Ivan to complete the job. If the total job is denoted by 1, then $\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ are the parts of the job that Tomislav, Krešimir, Ivan would complete, respectively, in one day. According to the conditions of the problem, we have the following equations:

$$
\left\{\begin{array}{l}
\frac{1}{x}+\frac{1}{y}=\frac{1}{20} \\
\frac{1}{y}+\frac{1}{z}=\frac{1}{15} \\
\frac{1}{x}+\frac{1}{z}=\frac{1}{12}
\end{array}\right.
$$

We need to solve this system of linear equations.

By adding these three equations, after simplification, we get

$$
\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{10}
$$

Working together, they would complete $\frac{1}{10}$ of the total job in one day, i.e., the entire job would be completed in 10 days.

Now we have:

$$
\frac{1}{x}=\frac{1}{10}-\left(\frac{1}{y}+\frac{1}{z}\right)=\frac{1}{10}-\frac{1}{15}=\frac{1}{30} \quad \text { i.e. } \quad x=30
$$

Similarly, we get $y=60, z=20$. Therefore, Tomislav would complete the entire job in 30 days, Krešimir in 60 days, and Ivan in 20 days.