College Algebra & Trigonometry, 2018a

1.9. RATIONAL EQUATIONS 85
33) A group decides to build a cabin together. The job can be done by 3 skilled
workers in 4 days or by 5 amateurs in 6 days. How long would it take if they all
work together?
34) If it requires 18 workers 50 days to build a piece of road, how many days
sooner would it be done if 7 more workers were hired at the beginning of operations?
35) A contractor estimated that a certain piece of work would be done by 9
carpenters in 8 hours or by 16 amateurs in 9 hours. The contractor wishes to get
the job done as quickly as possible and uses both professional carpenters and
amateurs on the same job. Four carpenters and 4 amateurs begin work at 6am.
Allowing 45 minuntes for lunch, at what time should they finish the job?
36) Mrs. Ellis alone can do a piece of work in 6 days. Her oldest daughter
takes 2 days longer; her youngest daughter takes twice as long as her mother.
How long will it take to complete the job if all three work together?
37) If 5 men and 2 boys work together, a piece of work can be completed in
one day and if 3 men and 6 boys work together, it can be completed in one day.
How long would it take a boy to do the work alone?
38) A coal company can fill a certain order from one mine in 3 weeks and from
a second mine in 5 weeks. How many weeks would be required to fill the order
if both mines were used?
39) If 25 skilled workers work for 8 days, they can complete the construction
of a concrete dam; 12 skilled workers and 15 untrained workers together can
complete the dam in 10 days. How long would it take an untrained worker alone
to complete the work on the dam?