ANSWER
Paul and Matt will take
[tex]9.9 \: \: hours[/tex]
to install the floor working together.
EXPLANATION
First, calculate Paul's rate, which is
[tex] = \frac{1}{18} [/tex]
Next, calculate Matt's rate, which is,
[tex] = \frac{1}{22} [/tex]
Let us assume that, Paul and Matt took
[tex]x \: hours[/tex]
to do the work together.
Then, the rate of working together is,
[tex] = \frac{1}{x} [/tex]
Now, add the individual rates and equate to the rate of working together to form an equation that will help us solve for x.
[tex] \frac{1}{18} + \frac{1}{22} = \frac{1}{x} [/tex]
Simplify the left hand side
[tex] \frac{11 + 9}{198} = \frac{1}{x} [/tex]
[tex] \frac{20}{198} = \frac{1}{x} [/tex]
We reciprocate both sides to get (You could have also done cross multiplication).
[tex] \frac{198}{20} = \frac{x}{1} [/tex]
[tex]x = 9.9 \: hours[/tex]
