Answer
$108 \text{ dollars}$
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}{6}+\dfrac{1}{4}=\dfrac{1}{x}
.\end{array}
Using the $LCD=12x$ and the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
12x\left(\dfrac{1}{6}+\dfrac{1}{4}\right)=\left(\dfrac{1}{x}\right)12x
\\\\
2x(1)+3x(1)=12(1)
\\\\
5x=12
\\\\
x=\dfrac{12}{5}
.\end{array}
Hence, the time it takes to finish the job when both work together is $\dfrac{12}{5}$ hours. At a labor cost of \$$45.00$ per hour, then the labor estimate is
\begin{array}{l}\require{cancel}
\dfrac{12}{5}(45)
\\\\=
108 \text{ dollars}
.\end{array}
