3. "Sasho and I, said Darko, can finish a job in 20 days, but if I work with Nikola instead of Sasho, the job will be completed in 15 days."

"I have a better combination, said Nikola, if I take Sasho as a helper, then we will finish the job in 12 days."

How many days will each of them take to finish the job on their own?
Solution. Let's assume that Sasho needs $s$ days, Darko needs $d$ days, and Nikola needs $n$ days to complete the work alone. Considering how much work each of them completes in one day, we get the system of equations

$$
\frac{1}{d}+\frac{1}{s}=\frac{1}{20}, \frac{1}{d}+\frac{1}{n}=\frac{1}{15}, \frac{1}{n}+\frac{1}{s}=\frac{1}{12}
$$

By adding these equations, we get

$$
\frac{2}{d}+\frac{2}{n}+\frac{2}{s}=\frac{12}{60}, \text { i.e. } \frac{1}{d}+\frac{1}{n}+\frac{1}{s}=\frac{1}{10}
$$

Now, if we subtract each of the equations in the system from the last equation one by one, we get $\frac{1}{n}=\frac{1}{20}, \frac{1}{s}=\frac{1}{30}, \frac{1}{d}=\frac{1}{60}$. Therefore, if working alone, Sasho will complete the work in 30 days, Darko in 60 days, and Nikola in 20 days.