SOLUTION: John paints a wall 6 hours longer then matt does. Together they paint a wall in 4 hours. How long does it take for each to paint the wall if they did it alone.

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Question 548776: John paints a wall 6 hours longer then matt does. Together they paint a wall in 4 hours. How long does it take for each to paint the wall if they did it alone.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
John paints a wall 6 hours longer then matt does. Together they paint a wall in 4 hours. How long does it take for each to paint the wall if they did it alone.
We make this chart

                            Number of         Number of       Rate in
                          walls painted    hours required     walls/hr
John painting alone

Matt painting alone

Both painting together

Suppose Matt takes x hours to paint 1 wall. 
Then John takes x+6 hours to paint 1 wall.
Together it takes them 4 hours to paint 1 wall.
Fill those in

                            Number of         Number of       Rate in
                          walls painted    hours required     walls/hr
John painting alone             1               x+6 

Matt painting alone             1                x

Both painting together          1                4


Next fill in the rates in walls/hr by dividing number of walls painted
by the hours required:

                            Number of         Number of       Rate in
                          walls painted    hours required     walls/hr
John painting alone             1               x+6           1%2F%28x%2B6%29  
Matt painting alone             1                x             1%2Fx   
Both painting together          1                4             1%2F4


           The equation comes from

                %28matrix%284%2C1%2C%22John%27s%22%2Crate%2Cpainting%2Calone%29%29 + %28matrix%284%2C1%2C%22Matt%27s%22%2Crate%2Cpainting%2Calone%29%29 = %28matrix%285%2C1%2Ctheir%2Ccombined%2Crate%2Cpainting%2Ctogether%29%29

                           1%2F%28x%2B6%29 + 1%2Fx = 1%2F4

Solve that and get x = 6

So Matt takes 6 hours and John takes x+6 or 6+6 or 12 hours.

Edwin