SOLUTION: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to pain the house together?

If Sally can paint a house in 4 hours, and John can paint 
the same house in 6 hours, how long will it take for both 
of them to paint the house together?

Let x = the answer, i.e., the number of hours it will take 
both of them to paint the hous working together. 

The secret to this type of problem is to

1. ask yourself this question for each person: 

"What fraction of a job can this person do in just ONE 
unit of time?"

2. Then after answering that ask yourself this for each 
person:

"Therefore what fraction of a job can this person do in 
x units of time?" 

=========================================================

We read this:

>>...Sally can paint a house in 4 hours...<<

1. so we ask ourselves this question:

What fraction of a house each can she paint in just ONE 
hour?

Since she can paint a whole house in 4 hours, then in 
only ONE hour, she can paint 1/4 of a house.

2. Then, having answered that we ask this question:

"Therefore what fraction of a house can she paint in x 
hours?"

Since she can paint 1 fourth  (1/4) of a house in 1 hour,
      she can paint x fourths (x/4) of a house in x hours.

Now we aske the same questions about John:

We read this about John:

>>...John can paint the same house in 6 hours...<<

1. so we ask ourselves this question:

What fraction of a house each can he paint in just ONE 
hour?

Since he can paint a whole house in 6 hours, then in only 
ONE hour, she can paint 1/6 of a house.

2. Then, having answered that we ask this question:

"Therefore what fraction of a house can he paint in x 
hours?"

Since he can paint 1 sixth  (1/6) of a house in 1 hour,
      he can paint x sixths (x/6) of a house in x hours.

=======================================

Now we reason this way:

The fraction of a house that she paints in x hours +
    The fraction of a house that he paints in x hours =
        1 house painted

So, x/4 + x/6 = 1

Can you solve that by first multiplying by LCD = 12?

If not, post again.

If you solve that you get x = 12/5
 or 2.4 hours or 2 hours 24 minutes.

Edwin