Answer
$8 \text{ mph}$
Work Step by Step
Let $x$ be the rate of the current.
Using $D=rt,$ then for upstream,
\begin{array}{l}\require{cancel}
72=(32-x)t
\\\\
\dfrac{72}{32-x}=t
.\end{array}
Using $D=rt,$ then for downstream,
\begin{array}{l}\require{cancel}
120=(32+x)t
\\\\
\dfrac{120}{32+x}=t
.\end{array}
Equating the two expressions of $t$ and using the properties of equality, then
\begin{array}{l}\require{cancel}
\dfrac{72}{32-x}=\dfrac{120}{32+x}
\\\\
72(32+x)=120(32-x)
\\
2304+72x=3840-120x
\\
72x+120x=3840-2304
\\
192x=1536
\\
x=\dfrac{1536}{192}
\\\\
x=8
.\end{array}
Hence, the rate of the current, $x,$ is $
8 \text{ mph}
.$
