SOLUTION: A welder requires 24 h to do a job. After the welder and an apprentice work on the job for 12 h, the welder quits. The apprentice finishes the job in 15 h. How long would it take t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A welder requires 24 h to do a job. After the welder and an apprentice work on the job for 12 h, the welder quits. The apprentice finishes the job in 15 h. How long would it take t      Log On


   

Question 1028976: A welder requires 24 h to do a job. After the welder and an apprentice work on the job for 12 h, the welder quits. The apprentice finishes the job in 15 h. How long would it take the apprentice, working alone, to do the job?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
List of the work rates:
welder                   1%2F24

apprentice               1%2Fx

welder + apprentice      1%2Fx%2B1%2F24

The example is a uniform work rates problem, like RT=J, using J for amount of job.
Put the description into an equation.
highlight_green%28%281%2Fx%2B1%2F24%29%2A12%2B%281%2Fx%2915=1%29

That is enough help unless you need help with the algebra. Solve for x.
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Yes, you want more help on solving the equation...



You should be able to identify the simplest common denominator being 24x. You can begin by MULTIPLYING the left and right members by 24x.

24x%282%2Fx%2B1%2F24%29%2A12%2B24x%281%2Fx%29%2A15=24x%2A1

24x%2A12%2A2%2Fx%2B24x%2A12%2F24%2B24x%2A15%2Fx=24x

24%2A12%2A2%2B12x%2B24%2A15=24x

24%2A12%2A2%2B24%2A15%2B12x=24x

24%2A12%2A2%2B24%2A15=12x

%2824%2A12%2A2%2B24%2A15%29%2F12=x

2%2A12%2A2%2B2%2A15=x

x=48%2B30

highlight%28x=79%29-------------No!

The steps above contain a mistake, not yet found. After working again on paper, the result found is highlight%28x=54%29, and this checks as correct when substituted in the original equation.