Question 1145949
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Let x be the time for Jeff to do the job alone.


Then the rate of work for Jeff is  {{{1/x}}}  of the job per hour;

                      for Kirk  {{{1/(x+2)}}}  of the job per hour,  an

                      the combined rate of work for both is  {{{1/12}}}  of the hour.


It gives you an equation


    rate of Jeff + rate of Kirk = combined rate,   or


       {{{1/x}}}        +   {{{1/(x+2)}}}       = {{{1/12}}}.


To solve the equation, multiply both sides by  12x(x+2).  You will get


     12(x+2) + 12x = x(x+2)

     12x + 24 + 12x = x^2 + 2x

     x^2 - 22x - 24 = 0.


Apply the quadratic formula

     
{{{x[1,2]}}} = {{{(22 +- sqrt((-22)^2 +4*24))/2}}} = {{{(22 +- 24.083)/2}}}.


Only positive root  x= 23.0415  makes sense.


<U>Answer</U>.  23.04 hours for Jeff  and  25.04 hours for Kirk.


<U>CHECK</U>.   {{{1/23.0415 + 1/25.0415}}} = 0.083334;  {{{1/12}}} = 0.083333.   ! Correct !
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Solved.