Question 890117
Let x = time for Tracy to buff the floor.
Their work rates are:
Brent, {{{1/(x+2)}}}
Tracy, {{{1/x}}}


The language used means that each of them works on the job separately not at the same time.


{{{(1/(x+2))3+(1/x)*2=1}}}, their work accounts for one whole job of buffing the floor.
{{{3/(x+2)+2/x=1}}}
{{{3x+2(x+2)=x(x+2)}}} after multiplying both sides by the common denominator x(x+2).
{{{3x+2x+4=x^2+2x}}}
{{{3x+4=x^2}}}
{{{x^2-3x-4=0}}}
{{{(x+1)(x-4)=0}}}
The solution which has meaning is {{{highlight(x=4)}}}, the time for Tracy to do one whole job done alone.