SOLUTION: A plumber made 600 dollars for working on a certain job. His apprentice who makes 3 dollars per hour less also made 600 dollars, but he worked 10hours more than the plumber. How mu

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Question 1032239: A plumber made 600 dollars for working on a certain job. His apprentice who makes 3 dollars per hour less also made 600 dollars, but he worked 10hours more than the plumber. How much did the plumber make per hr?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the plumber's charge/hr
Let +t+ = time in hours the plumber worked
-------------------
Plumber's equation:
(1) +c+=+600%2Ft+
Apprentice's equation:
(2) +c+-+3+=+600%2F%28+t+%2B+10+%29+
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Substitute (1) into (2)
(2) +600%2Ft+-+3+=+600%2F%28+t+%2B+10+%29+
Multiply both sides by +t%2A%28+t+%2B+10+%29+
(2) +600%2A%28+t+%2B+10+%29+-+3%2At%2A%28+t+%2B+10+%29+=+600t+
(2) +600t+%2B+6000+-+3t%5E2+-+30t+=+600t+
(2) +3t%5E2+%2B+30t+-+6000+=+0+
(2) +t%5E2+%2B+10t+-+2000+=+0+
I note that +2000+=+40%2A50+
(2) +%28+t+%2B+50+%29%2A%28+t+-+40+%29+
+t+=+40+
and
(1) +c+=+600%2Ft+
(1) +c+=+600%2F40+
(1) +c+=+15+
The plumber made $15/hr
( this must be on some other planet! )
------------------------
check:
(2) +c+-+3+=+600%2F%28+t+%2B+10+%29+
(2) +15+-+3+=+600%2F%28+40+%2B+10+%29+
(2) +12+=+600%2F50+
(2) +12+=+12+
OK