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

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

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

`(1)/(x) = (1)/(8) + (1)/(6)`

`(1)/(x) = (3 + 4)/(24)`

`(1)/(x) = (7)/(24)`

`7x = 24`

`x = (24)/(7)`

`x = 3.43`

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