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

Algebra ->  Human-and-algebraic-language -> 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       Log On


   

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) About Me  (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  1%2Fx  of the job per hour;

                      for Kirk  1%2F%28x%2B2%29  of the job per hour,  an

                      the combined rate of work for both is  1%2F12  of the hour.


It gives you an equation


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


       1%2Fx        +   1%2F%28x%2B2%29       = 1%2F12.


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%5B1%2C2%5D = %2822+%2B-+sqrt%28%28-22%29%5E2+%2B4%2A24%29%29%2F2 = %2822+%2B-+24.083%29%2F2.


Only positive root  x= 23.0415  makes sense.


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


CHECK.   1%2F23.0415+%2B+1%2F25.0415 = 0.083334;  1%2F12 = 0.083333.   ! Correct !

Solved.