SOLUTION: Twenty people working 9 hours per day are needed to complete a large sorting job within ten days. How many hours per day would eighteen people need to have worked to complete the j

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Question 849367: Twenty people working 9 hours per day are needed to complete a large sorting job within ten days. How many hours per day would eighteen people need to have worked to complete the job within the same time?
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
20*9*10=180*10 worker hours for ten days
180/18=10
They would have to work 10 hours a day for ten days

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
1/10 as many people would take 10 times
longer to do the same job, so
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+%281%2F10%29%2A20+=+2+ people take +90%2A10+=+900+
hours to do the same job
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The rate that the 20 people work is ( 1 job ) / ( 90hrs )
= +1%2F90+
The rate that the 2 people work is ( 1 job ) / ( 900 hrs )
= +1%2F900+
----------------------------------------------
Let ( 1 job ) / ( h hours ) = +1%2Fh+ = the rate that
18 people work
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I can then say:
+1%2F90+-+1%2F900+=+1%2Fh+
Multiply both sides by +900h+
+10h+-+h+=+900+
+9h+=+900+
+h+=+100+
---------------
( 100 hrs ) / ( 10 days ) = 10 hrs / day
So, 18 people need to work 10 hrs a day to
finish the job in 10 days