For a certain task, $B$ needs 6 more days than $A$, and $C$ needs 3 more days than $B$. If $A$ works for 3 days and $B$ works for 4 days together, they accomplish as much as $C$ does in 9 days. How many days would each take to complete the task alone?
If $A$ completes the work in $x$ days, then $B$ completes it in $x+6$ days and $C$ in $x+9$ days. According to the problem,

$$
3 \cdot \frac{1}{x}+4 \cdot \frac{1}{x+6}=9 \cdot \frac{1}{x+9}
$$

or

$$
\begin{gathered}
3(x+6)(x+9)+4 x(x+9)=9 x(x+6) \\
2 x^{2}-27 x-162=0
\end{gathered}
$$

from which the positive value of $x$ is 18, so $y=24$ and $z=27$.