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?

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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?
Found 3 solutions by Edwin McCravy, stanbon, Alan3354:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
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
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
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?
----
Sara rate: 1/2 job/hr
Dan rate:: 1/4 job/hr
---
Together rate: 1/x job/hr
------
Equation:
rate + rate = together rate
1/2 + 1/4 = 1/x
Multiply thru by 4x to get:
2x + x = 4
3x = 4
x = 3/4 hr. (time to do the job together)
==============
Cheers,
Stan H.
================
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Also, there's a shortcut, it's product/sum
2*4/(2+4) = 8/6
= 4/3 hours
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