SOLUTION: A plumber works twice as fast as his apprentice. After the plumber has worked alone for 3 hours, his apprentice joins him and working together they complete the job 4 hours later.

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Question 1119209: A plumber works twice as fast as his apprentice. After the plumber has worked alone for 3 hours, his apprentice joins him and working together they complete the job 4 hours later. How many hours would it have taken the plumber to do the entire job by himself?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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..., worked alone for 3 hours, his apprentice joins him and working together they complete the job 4 hours later....
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%282%2Fx%293%2B%282%2Fx%2B1%2Fx%294=1
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6%2Fx%2B4%283%2Fx%29=1
18%2Fx=1
highlight%28x=18%29------the apprentice
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18%2F2=highlight%289%29----time for plumber, one job

Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.
The correct answer is 9 hours for the plumber to make the job working alone.

Solution 

Let  r be the rate of of work of the apprentice.


Then the plumber's rate of work is 2r.


After working 3 hours alone, the plumber completed  3*(2r)  pars of the entire job.


When the apprentice joined him, they worked 4 more hours and made 4*(2r+r) = 12r  parts of the job.


For the entire job you have this equation


    3*(2r) + 12r = 1,   or

    18r  = 1.


It means  r = 1%2F18,  i.e.  apprentice can make the job in 18 hours working alone.


Since the plumber works two times faster, he needs only 9 hours.

Solved.