SOLUTION: It takes Sara 2 hours to paint a fence and Daniel 4 hours to paint the same fence. How long will it take to paint the fence if they work together?

Make the chart:

                  Number of        Time         Rate
                   fences        required        in
                   painted       in hours    fences/hour
Sara alone
Daniel alone
Both together

Let x be the number of hours required for both painting together
to paint 1 fence. Also we fill in the times required that are 
given in each of the other two cases to paint 1 fence.  Also
we fill in 1 for the number of fences, since in each case only
1 fence is painted:

                  Number of        Time         Rate
                   fences        required        in
                   painted       in hours    fences/hour
Sara alone            1             2
Daniel alone          1             4
Both together         1             x

We finish the table by filling in the rates in fences/hour by 
dividing the number of fences painted by the number of hours 
required in each case:

                  Number of        Time         Rate
                   fences        required        in
                   painted       in hours    fences/hour
Sara alone            1             2             1/2
Daniel alone          1             4             1/4  
Both together         1             x             1/x
  
The equation comes from:

                   


                            +  = 

Solve that by first clearing of fractions by multiplying both
sides by LCD of 4x.

Answer x =  or  hours or 1 hour and 20 minutes.

Edwin