SOLUTION: Jeff and Kirk can build a​ 75-ft retaining wall together in 5 hours. Because Jeff has more​ experience, he could build the wall by himself 2 hours quicker than Kirk. How long

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Question 1145949: Jeff and Kirk can build a​ 75-ft retaining wall together in 5 hours. Because Jeff has more​ experience, he could build the wall by himself 2 hours quicker than Kirk. How long would it take Kirk​ (to the nearest​ minute) to build the wall by​ himself?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

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


Then the rate of work for Jeff is    of the job per hour;

                      for Kirk    of the job per hour,  an

                      the combined rate of work for both is    of the hour.


It gives you an equation


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


               +          = .


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

     
 =  = .


Only positive root  x= 23.0415  makes sense.


Answer.  23.04 hours for Jeff  and  25.04 hours for Kirk.


CHECK.    = 0.083334;   = 0.083333.   ! Correct !

Solved.


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