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.
<pre>
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/(x+6)}}}  
Matt painting alone             1                x             {{{1/x}}}   
Both painting together          1                4             {{{1/4}}}


           The equation comes from

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

                           {{{1/(x+6)}}} + {{{1/x}}} = {{{1/4}}}

Solve that and get x = 6

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

Edwin</pre>