Question 890914
Koko can paint a room two hours less than Andre. 
<pre>
Suppose Andre cn paint a room in x hours.

Then Koko can pain a room in x-2 hours

So Andre's painting rate is 1 room per x hours or {{{matrix(1,2,1,room)/matrix(1,2,x,hours)}}} or {{{matrix(1,2,1/x,rooms/hour)}}}

And Koko's painting rate is 1 room per x-2 hours or {{{matrix(1,2,1,room)/matrix(1,2,x-2,hours)}}} or {{{matrix(1,2,1/(x-2),rooms/hour)}}}
</pre>
If they will work together, they can finish the job in 12 hours. 
<pre>
So their combined painting rate is 1 room per 12 hours or {{{matrix(1,2,1,room)/matrix(1,2,12,hours)}}} or {{{matrix(1,2,1/12,rooms/hour)}}}

The equation comes from 

      {{{(matrix(3,1,"Andre's", painting, rate))}}}{{{""+""}}}{{{(matrix(3,1,"Koko's", painting, rate))}}}  {{{""=""}}}  {{{(matrix(4,1,Their,combined,painting, rate))}}}

   {{{1/x}}}{{{""+""}}}{{{1/(x-2)}}} {{{""=""}}} {{{1/12}}}

Multiply through by LCD of 12x(x-2)

   {{{12(x-2)+12x}}}{{{""=""}}}{{{x(x-2)}}}

   {{{12x-24+12x}}}{{{""=""}}}x^2-2x}}}

        {{{24x-24}}}{{{""=""}}}x^2-2x}}}

           {{{0}}}{{{""=""}}}{{{x^2-26x+24}}}

That doesn't factor, so

          {{{x}}}{{{""=""}}}{{{(-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

          {{{x}}}{{{""=""}}}{{{(-(-26) +- sqrt((-26)^2-4*(1)*(24) ))/(2*(1)) }}}

          {{{x}}}{{{""=""}}}{{{(26 +- sqrt(676-96) )/2 }}}

          {{{x}}}{{{""=""}}}{{{(26 +- sqrt(580) )/2 }}}

Solutions x=25.04159458 and 0.9584054212

The second answer makes no sense since (1) we can't subtract 2 from it and
get a positive answer, and (2) if Andre being able to finish in less than 
an hour makes no sense. :)

Answer:  It would take Andre a little over 25 hours and Koko a little 
over 23 hours.

Edwin</pre>