SOLUTION: a welder requires 24 hours to do a job. after the welder and apprentice work on the job for 12 hours, the welder quits. the apprentice finished the job in 9 hours. how long would

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Question 1025775: a welder requires 24 hours to do a job. after the welder and apprentice work on the job for 12 hours, the welder quits. the apprentice finished the job in 9 hours. how long would it take the apprentice, working alone, to do the job?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) (Show Source):
You can put this solution on YOUR website!

WORKER RATE in JOB/HOUR Welder Apprenctice Both Combined

Unknown time p for the apprenctice, like a pupil, to do the 1 job. Simplify the combined
rate.

The described situation is welder and apprentice together for 12 hours, and then just the
apprenctice for 9 hours to finish. One job done.

Uniform work rates rule goes as RT=W for RATE, TIME, WORK. Here, the amount of "work" done
is 1 job. One whole job.

-------Be sure this makes sense for you.

Simplest common denominator is .
Multiply left and right sides of the equation by , simplify, and solve for p.

Answer by ikleyn(52884) (Show Source):
You can put this solution on YOUR website!
.
a welder requires 24 hours to do a job. After the welder and apprentice work on the job for 12 hours, the welder quits. The apprentice finished the job in 9 hours. How long would it take the apprentice, working alone, to do the job?
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Let a = the rate-of-work (in units of ) of the apprentice. We know that the welder's rate-of-work is of the job-per-hour. The balance equation is = . Simplify it: 9a = - 12a, 21a = , a = = . Hence, it will take 42 hours for the apprentice to complete the job working alone.