Answer
$\dfrac{20}{9} \text{ hours}$
Work Step by Step
Let $x$ be the time it takes to finish the job when both work together.
In terms of $1$ part/unit, the rates are related as
\begin{array}{l}\require{cancel}
\dfrac{1}{4}+\dfrac{1}{5}=\dfrac{1}{x}
.\end{array}
Using the $LCD=20x$ and the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
20x\left(\dfrac{1}{4}+\dfrac{1}{5}\right)=\left(\dfrac{1}{x}\right)20x
\\\\
5x(1)+4x(1)=20(1)
\\\\
5x+4x=20
\\\\
9x=20
\\\\
x=\dfrac{20}{9}
.\end{array}
Hence, the time it takes to finish the job when both work together is $
\dfrac{20}{9} \text{ hours}
.$
