2. In a garden partnership, they decided to make a pond using water from a spring. All the water from the spring was directed into the pond using a pipeline, and the pond began to fill with water. As a result, after \( t = 16 \) days, the pond was filled to \( 2 / 3 \) of its volume. At this moment, it was noticed that one quarter of the water from the spring was leaking through the pipeline. The leaks were fixed. How long after this did the pond fill up?
2. Let the volume of the pond be $V$, and the volume of water flowing out of the source per unit time be $w$. Since before the leak was sealed, three-quarters of the water from the spring entered the pond, we have

$$
\frac{3}{4} w t = \frac{2}{3} V \quad \Rightarrow \quad \frac{9}{8} t = \frac{V}{w}
$$

![](https://cdn.mathpix.com/cropped/2024_05_06_0e208de39d119289f7e1g-1.jpg?height=591&width=836&top_left_y=367&top_left_x=1087)

After the leak was sealed, all the water started entering the pond. Therefore, for the time $t_{1}$ required to completely fill the pond, we have

$$
w t_{1} = \frac{1}{3} V \quad \Rightarrow \quad 3 t_{1} = \frac{V}{w}
$$

By equating the left sides of these equations, we get

$$
t_{1} = \frac{3}{8} t
$$