SOLUTION: if sally can paint a house in 4hrs and john can paint the same house in 6hrs, how long will it take for both of them to paint the house together

The easy way to do it is this way, which you can do in your head:

4 and 6 both go into 12.  In 12 hours Sally can paint 3 houses and
John can paint 2 houses.  So that's 5 houses in 12 hours, or 1 house
in  hours or  hours, or 2 hours 24 minutes.

But your teacher doesn't want you to do it that easy way.  

Your teacher wants you to make this chart, get an equation 
and solve it:

          number        time        rate in
            of         required     houses
          houses         in          per  
          painted       hours        hour
--------|-----------|-----------|----------
Sally   |           |           |
--------|-----------|-----------|----------
John    |           |           |  
--------|-----------|-----------|----------
Both    |           |           | 
--------|-----------|-----------|---------- 


Let x be the number of hours required for both.
So fill in x in the middle on the bottom row,
for the time for both to paint one house working
together.

          number        time        rate in
            of         required     houses
          houses         in          per  
          painted       hours        hour
--------|-----------|-----------|----------
Sally   |           |           |
--------|-----------|-----------|----------
John    |           |           |  
--------|-----------|-----------|----------
Both    |           |     x     | 
--------|-----------|-----------|---------- 
  
Next fill in the times, 4 for Sally and 6 for John


          number        time        rate in
            of         required     houses
          houses         in          per  
          painted       hours        hour
--------|-----------|-----------|----------
Sally   |           |     4     |
--------|-----------|-----------|----------
John    |           |     6     |  
--------|-----------|-----------|----------
Both    |           |     x     | 
--------|-----------|-----------|---------- 

We are only talking about them painting 1 house so we
fill in 1 for the number of houses painted in all three
cases:

          number        time        rate in
            of         required     houses
          houses         in          per  
          painted       hours        hour
--------|-----------|-----------|----------
Sally   |     1     |     4     |
--------|-----------|-----------|----------
John    |     1     |     6     |  
--------|-----------|-----------|----------
Both    |     1     |     x     | 
--------|-----------|-----------|----------

Next we fill in the rates in houses/hour by
dividing the number of houses by the number
of hours

          number        time        rate in
            of         required     houses
          houses         in          per  
          painted       hours        hour
--------|-----------|-----------|----------
Sally   |     1     |     4     |    
--------|-----------|-----------|----------
John    |     1     |     6     |    
--------|-----------|-----------|----------
Both    |     1     |     x     |    
--------|-----------|-----------|---------- 

Then we form the equation from:

       (Sally's rate) + (John's rate) = (rate for both together)
                          
                                  
 Multiply through by LCD = 12x
                         
                                                             
                                   

                                    
or  hours, or 2 hours 24 minutes 

Edwin