SOLUTION: 8 workers working at the same rate can finish some work in 16 days.After working for 4 days,2 workers felt sick and never turned back.How many days did the they take to complete th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 8 workers working at the same rate can finish some work in 16 days.After working for 4 days,2 workers felt sick and never turned back.How many days did the they take to complete th      Log On


   

Question 1125204: 8 workers working at the same rate can finish some work in 16 days.After working for 4 days,2 workers felt sick and never turned back.How many days did the they take to complete the work?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Say it like this:

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Eight workers, each working at the same rate, can finish a quantity of work in 16 days. After working for 4 days,2 workers felt sick and never returned back. How many days did the the remaining workers take to complete the work?
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r, the rate of 1 worker
8r%2A16=1, using "a quantity of work" as 1 whole piece of work.


The two separate numbers of workers for different time quantities, x for the unknown time quantity:
8r%2A4%2B6r%2Ax=1%2C+completing+the+work+with+the+6+remaining+workers
6rx=1-42r
6%281%2F%288%2A16%29%29x=1-32%281%2F%288%2A16%29%29
%283%2F%2864%29%29x=1-1%2F4
x=%281-1%2F4%29%2864%2F3%29
x=%283%2F4%29%2864%2F3%29
x=64%2F4
x=16
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A different try:
After the full eight worked for 4 days, 3%2F4 of the job still needed to be done. That is, 6 workers must work for x days to complete 3%2F4 of the job.
6r%2Ax=3%2F4
x=%283%2F4%29%281%2F6%29%281%2Fr%29
x=%281%2F8%29%281%2Fr%29
x=%281%2F8%29%288%2A16%29
highlight%28x=16%29

16 more days