3. Workers Andrej, Boris, and Tsane collectively complete a job in 1 hour. It is known that each of them completes the same job in a whole number of hours. In addition, it is known that Boris works faster than Andrej, but slower than Tsane. How many hours will it take for each of the three workers to complete the job working alone?
Solution. Let's assume that Andrej can finish the work alone in $a$ hours, Boris in $b$ hours, and Tsan in $c$ hours. Then in 1 hour, they will complete $\frac{1}{a}, \frac{1}{b}$, and $\frac{1}{c}$ of the work, respectively. Since they complete the work together in 1 hour, we get $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$. However, $a, b, c$ are natural numbers for which $c<b<a$ holds, so it easily follows that $a=6, b=3, c=2$ hours.