Question 512923
 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?
<pre>

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:

                  {{{(matrix(4,1,
                   "Sara's", 
                   rate,
                   painting,
                   alone))+(matrix(4,1,
                   "Daniel's", 
                   rate,
                   painting,
                   alone))=(matrix(5,1,
                   their, 
                   combined,
                   rate,
                   painting,
                   together))}}} 


                           {{{1/2}}} + {{{1/4}}} = {{{1/x}}}

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

Answer x = {{{4/3}}} or {{{1&1/3}}} hours or 1 hour and 20 minutes.

Edwin</pre>