13.172. Two vessels with salt solutions were set for evaporation. The daily evaporated portions of salt are constant for each vessel. From the first vessel, 48 kg of salt was obtained, and from the second, which stood for 6 days less, 27 kg. If the first vessel had stood as many days as the second, and the second as many days as the first, then the same amount of salt would have been obtained from both solutions. How many days did each solution stand?
## Solution.

Let $x$ be the number of days the first solution stood, and $y$ be the number of days the second solution stood. The daily evaporated portion for the first container is $\frac{48}{x}$ kg of salt, and for the second container, it is $\frac{27}{y}$ kg. According to the problem, we have the system of equations $\left\{\begin{array}{l}\frac{48}{x} \cdot y=\frac{27}{y} \cdot x, \\ y=x-6,\end{array}\right.$ from which we find $x=24$ days, $y=18$ days.

Answer: 18 and 24.