SOLUTION: an experienced plumber made $600 for working on a certain job. his apprentice, who makes $3 per hour less, also made $600. however, the apprentice worked 10 h more than the plumber

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Question 253119: an experienced plumber made $600 for working on a certain job. his apprentice, who makes $3 per hour less, also made $600. however, the apprentice worked 10 h more than the plumber. how much does the plumber make per hour?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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an experienced plumber made $600 for working on a certain job.
his apprentice, who makes $3 per hour less, also made $600.
however, the apprentice worked 10 h more than the plumber.
how much does the plumber make per hour?
:
Let x = amt per hour made by the plumber
then
(x-3) = amt made by the apprentice
:
Write a time equation: Time = 600%2F%28hourly+pay%29
:
Plumbers time = Appren time - 10 hrs
600%2Fx = 600%2F%28%28x-3%29%29 - 10
Multiply equation by x(x-3); results
600(x-3) = 600x - 10x(x-3)
600x - 1800 = 600x - 10x^2 + 30x
:
Combine on the left to form a quadratic equation
10x^2 - 30x + 600x - 600x - 1800 = 0
10x^2 - 30x - 1800 = 0
:
simplify, divide by 10
x^2 - 3x - 180 = 0
Factors
(x - 15)(x + 12) = 0
positive solution
x = $15 per hr for the plumber
;
:
Check solution by finding the time of each
600/15 = 40 hrs
600/12 = 50 hrs, apprentice worked 10 hrs more