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Question 1125793: The foreman at a contracting company is distributing his employees to different
jobs this week. Each work day begins at 8am. He has one job in particular that must
be completed by 1pm on Monday. The foreman separates his workers into two categories,
experienced and inexperienced. The foreman estimates that an experienced worker could
complete the job in 9 hours on his own, and an inexperienced worker could complete the
job in 12 hours alone. Assume that no e_ciency is gained or lost when the employees
work together. Could two experienced workers complete the job in time? What about two
inexperienced workers? Can one experienced worker and one inexperienced worker complete
the job in time? If experienced workers are paid $26 per hour and inexperienced workers
are paid $12 per hour, and at least one experienced worker must be present at the job, what
should the foreman choose to do? Assume that workers are paid in hour increments, so that
if the job takes 5 hours and 10 minutes, everyone is paid for the full 6 hours.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! experienced does 1/9 of the job in an hour or x/9 of the job in x hours
inexperienced will do x/12 of the job in x hours
(x/9)+(x/12)=1 whole job
4x+3x=36
7x=36
x=36/7 or 5.14 hours or 5 hours and 8.5 minutes
An experienced and an inexperienced worker cannot finish the job in time.
x/9+x/9=1
2x=9
x=4.5 hours for experienced workers, and they can finish the job on time.
two inexperienced would require 6 hours using the same approach.
For a 5 hour deadline, the cost would be $130 per experienced worker, working 4.5 hours and being paid for 5, and double for 2 or $260.
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