Question 1025423
<pre>
Painter            Rate as ROOM/HOURS
Carl                 {{{1/(x-3)}}}
Jennifer             {{{1/x}}}
Both Combined        {{{1/2}}}</pre>


{{{highlight_green(1/(x-3)+1/x=1/2)}}}


{{{2x(x-3)(1/(x-3)+1/x)=2x(x-3)(1/2)}}}


{{{2x+2(x-3)=x(x-3)}}}


{{{2x+2x-6=x^2-3x}}}


{{{7x-6=x^2}}}


{{{x^2-7x+6=0}}}
(Yes, this IS factorable... see below.)


{{{x=(7+- sqrt(49-4*6))/2}}}

{{{x=(7+- sqrt(49-24))/2}}}


{{{x=(7+- 5)/2}}}


{{{x=system(1,OR,6)}}}---------but obviously one one of these can make any sense.


Jennifer paints the room herself in 6 hours.




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{{{x^2-7x+6}}}
{{{(x-6)(x-1)}}}