Answer
$1 \text{ hour}$
Work Step by Step
Let $x$ be the rowing speed.
Using $D=rt,$ then the conditions of the problem for rowing downstream is
\begin{array}{l}\require{cancel}
9=(x+6)t
\\\\
\dfrac{9}{x+6}=t
.\end{array}
Using $D=rt,$ then the conditions of the problem for rowing upstream is
\begin{array}{l}\require{cancel}
3=(x-6)t
\\\\
\dfrac{3}{x-6}=t
.\end{array}
Equating the two equation of $t,$ then
\begin{array}{l}\require{cancel}
\dfrac{9}{x+6}=\dfrac{3}{x-6}
.\end{array}
By cross-multiplication and by using the properties of equality, then
\begin{array}{l}\require{cancel}
9(x-6)=3(x+6)
\\\\
9x-54=3x+18
\\\\
9x-3x=18+54
\\\\
6x=72
\\\\
x=\dfrac{72}{6}
\\\\
x=12
.\end{array}
The time it takes to cover 9 miles downstream, $\dfrac{9}{x+6},$ is $0.5$ hour. The time it takes to cover 3 miles upstream, $\dfrac{3}{x-6},$ is $0.5$ hour. Hence, the total time to cover $12$ miles is $0.5+0.5=
1 \text{ hour}
.$
