Question

Adam and Judy own a painting company. To paint a particular house alone, Adam estimates that it would take him 8 days. Judy estimates that it would take her 6 days. If these estimates are accurate, how long should it take the two of them to paint the house if they work together?

Answer 1

Answer:

It should take 3.43 days for the two of them to paint the house if they work together.

Step-by-step explanation:

The together rate is the sum of each separate rate.

In this problem:

Together rate: 1/x

Adam's rate: 1/8

Judy's rate: 1/6.

So

Together rate = Adam's rate + Judy's rate

$\frac{1}{x} = \frac{1}{8} + \frac{1}{6}$

$\frac{1}{x} = \frac{3 + 4}{24}$

$\frac{1}{x} = \frac{7}{24}$

$7x = 24$

$x = \frac{24}{7}$

$x = 3.43$

It should take 3.43 days for the two of them to paint the house if they work together.