# Word problem: Sally can paint the house in 4 hours....

#### mamom

##### New member
Need help on how to solve this problem

Sally can paint the house in 4 hours. James can paint the house in 6 hours. If they paint it together how long will it take them?

#### Mrspi

##### Senior Member
Re: Word problem

mamom said:
Need help on how to solve this problem

Sally can paint the house in 4 hours. James can paint the house in 6 hours. If they paint it together how long will it take them?
If Sally can paint the house in 4 hours, then each hour, she paints 1/4 of the house.

If James can paint the house in 6 hours, then each hour, he paints 1/6 of the house.

Now, let x = number of hours they work together.

In x hours, Sally paints x/4 of the house, and James paints x/6 of the house.

And, what they do together in that x hours is the whole house!

So,

(x / 4) + (x / 6) = 1

Solve that for x....(hint: multlply both sides of the equation by the common denominator for the fractions)

is this right?

3x/12 + 2x/12 =1
5x/12=1
5x=12
x=2.4 hours

#### Denis

##### Senior Member
Yes mom: correct :idea: