Answer
$36 \text{ minutes}$
Work Step by Step
Let $x$ be the time (in minutes) it takes for the second hose to fill the pond alone.
In terms of $1$ unit/part, the rates are related as
\begin{array}{l}\require{cancel}
\dfrac{1}{45}+\dfrac{1}{x}=\dfrac{1}{20}
.\end{array}
Using the $LCD=
180x
$ and the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
180x\left(\dfrac{1}{45}+\dfrac{1}{x}\right)=\left(\dfrac{1}{20}\right)180x
\\\\
4x(1)+180(1)=9x(1)
\\\\
4x+180=9x
\\\\
180=9x-4x
\\\\
180=5x
\\\\
\dfrac{180}{5}=x
\\\\
x=36
.\end{array}
Hence, the second hose can fill the pond alone in $x,$ or $
36 \text{ minutes}
.$
