Answer
$\dfrac{10}{3} \text{ hours}$
Work Step by Step
Let $x$ be the time it takes for Dick to do the job alone.
In terms of $1$ unit/part, the rates are related as
\begin{array}{l}\require{cancel}
\dfrac{1}{5}+\dfrac{1}{x}=\dfrac{1}{2}
.\end{array}
Using the $LCD=
10x
$ and the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
10x\left(\dfrac{1}{5}+\dfrac{1}{x}\right)=\left(\dfrac{1}{2}\right)10x
\\\\
2x(1)+10(1)=5x(1)
\\\\
2x+10=5x
\\\\
10=5x-2x
\\\\
10=3x
\\\\
\dfrac{10}{3}=x
.\end{array}
Hence, Dick can do the job alone in $x,$ or $
\dfrac{10}{3} \text{ hours}
.$
