Respuesta :
The situation can be expressed in an equation system
Let V be the total volume of the pool, then
[tex]\begin{gathered} 16x=V \\ 20y=V \end{gathered}[/tex]with x, y in volume per time (x is the speed with which the pool is being filled, y the speed with which the water is being drained)
[tex]\begin{gathered} \Rightarrow16x=20y \\ \Rightarrow\frac{y}{x}=\frac{16}{20}=\frac{4}{5} \\ \Rightarrow y=\frac{4}{5}x \end{gathered}[/tex]So, the speed with which the water escapes from the pool is 4/5 of the speed with which the pool is being filled
[tex]\begin{gathered} t(x-y)=V \\ \Rightarrow t(x-\frac{4}{5}x)=V \\ \Rightarrow t(\frac{1}{5}x)=V \end{gathered}[/tex]Then,
[tex]\begin{gathered} t=\frac{V}{(\frac{1}{5}x)}, \\ \text{but 16x=V} \\ \Rightarrow t=\frac{16x}{(\frac{1}{5}x)} \\ \Rightarrow t=\frac{16}{\frac{1}{5}}=16\cdot5=80 \end{gathered}[/tex]Therefore, the pool will be completely filled in 80 hours
