Answer
$\dfrac{15}{8} \text{ hours}$
Work Step by Step
Let $x$ be the time it takes to finish the job when both scanners are working.
In terms of $1$ part/unit, the rates are related as
\begin{array}{l}\require{cancel}
\dfrac{1}{3}+\dfrac{1}{5}=\dfrac{1}{x}
.\end{array}
Using the $LCD=15x$ and the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
15x\left(\dfrac{1}{3}+\dfrac{1}{5}\right)=\left(\dfrac{1}{x}\right)15x
\\\\
5x(1)+3x(1)=15(1)
\\\\
5x+3x=15
\\\\
8x=15
\\\\
x=\dfrac{15}{8}
.\end{array}
Hence, the time it takes to finish the job when both scanners are working together, $x,$ is $
\dfrac{15}{8} \text{ hours}
.$
