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(39617)   (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(52782)  (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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