Answer
$\dfrac{4}{3} \text{ hours }$
Work Step by Step
Let $x$ be the hours for both printers operating together to finish the work. Expressed in $1$ unit/part, the rates are related as
\begin{array}{l}\require{cancel}
\dfrac{1}{4}+\dfrac{1}{2}=\dfrac{1}{x}
.\end{array}
Using the $LCD=
4x
,$ and the properties of equality, then
\begin{array}{l}\require{cancel}
4x\left( \dfrac{1}{4}+\dfrac{1}{2} \right) =\left( \dfrac{1}{x} \right)4x
\\\\
x+2x=4
\\\\
3x=4
\\\\
x=\dfrac{4}{3}
.\end{array}
Hence, it takes $
\dfrac{4}{3} \text{ hours }
$ for both printers operating together to finish the work.
