SOLUTION: A carpenter earned $720 for a certain job. Her apprentice also earned $720, but the apprentice earned $6 less per hour and worked 10 hours more than the carpenter. How much did the

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Question 1131150: A carpenter earned $720 for a certain job. Her apprentice also earned $720, but the apprentice earned $6 less per hour and worked 10 hours more than the carpenter. How much did the carpenter earn per hour?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
r, pay rate for the carpenter
r-6, pay rate for apprentice

x, time that carpenter worked
x+10, time that apprentice worked



Solve the system, especially for r.


Another Way: 
                  PAY RATE        TIME       PAY

Carpenter            r            720/r      720

Apprentice          r-6         720/(r-6)    720

DIFFERENCE                       10

--------solve for r.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Let x = the carpenter's hourly rate (in dollars), and h = time in hours the carpenter worked.


Then the apprentice's hourly rate is (x-6) dollars, and his (or her (?)) working time is (h+10) hours.


Then from the condition, you have this system of equations


    x*h = 720,              (1)
    (x-6)*(h+10) = 720      (2)


To solve the system, first FOIL equation (2). You will get


    xh - 6h + 10x - 60 = 720.    (3)


In (3), replace xh by 720, based on (1).  You will get


    720 - 6h + 10x - 60 = 720,   which is simplified to


    10x - 6h = 60.               (4)


Write equation (1) as  

    6xh = 6*720;                 (5)


from equation (4), express 6h = 10x - 60  and substitute it into equation (5).  You will get

    (10x - 60)*x = 6*720,

    10x^2 - 60x + 6*720 = 0,

    x^2 - 6x + 6*72 = 0,

    (x-24)*(x+18) = 0.


Of two solutions  x= 24  and  x= -18,  only positive solution  x= 24  is meaningful, giving the


ANSWER.  The carpenter's hourly rate is  $24 per hour.


CHECK.   The carpenter's working time is  h= 720/24 = 30 hours.


         The apprentice's hourly rate is  $24 - $6 = $18 and his (or her (?) ) working time is  30+10 = 40 hours.


         Both products  24*30  and  18*40  are equal to 720  dollars.   ! Correct !

Solved.


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