Question

Paul can install a 300 hundred square foot hardwood floor in 18 hours. Matt can install the same floor in 22 hours. How long would it take for Paul and Matt to install the floor working together?

Answer 1

ANSWER

Paul and Matt will take
$9.9 \: \: hours$
to install the floor working together.

EXPLANATION

First, calculate Paul's rate, which is

$= \frac{1}{18}$

Next, calculate Matt's rate, which is,
$= \frac{1}{22}$

Let us assume that, Paul and Matt took
$x \: hours$
to do the work together.

Then, the rate of working together is,

$= \frac{1}{x}$

Now, add the individual rates and equate to the rate of working together to form an equation that will help us solve for x.

$\frac{1}{18} + \frac{1}{22} = \frac{1}{x}$

Simplify the left hand side

$\frac{11 + 9}{198} = \frac{1}{x}$

$\frac{20}{198} = \frac{1}{x}$

We reciprocate both sides to get (You could have also done cross multiplication).

$\frac{198}{20} = \frac{x}{1}$

$x = 9.9 \: hours$