SOLUTION: it takes 5 workers 9 days to build a barn? how many days would it take 3 workers to build a barn? extra credit: if a the barn needs to be build in 7 days, what is the number of

Algebra ->  Rate-of-work-word-problems -> SOLUTION: it takes 5 workers 9 days to build a barn? how many days would it take 3 workers to build a barn? extra credit: if a the barn needs to be build in 7 days, what is the number of      Log On


   

Question 520556: it takes 5 workers 9 days to build a barn? how many days would it take 3 workers to build a barn?
extra credit:
if a the barn needs to be build in 7 days, what is the number of workers needed?
Found 2 solutions by oberobic, bucky:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
With job problems like this, it is best to look at the problem as a question of fractions.
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a crew of 5 workers can build a barn in 9 days
the crew builds 1/9 of the barn per day
each worker is 1/5 of the crew
each worker builds 1/45 of the barn per day
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5 workers * 1/45 barn/day * 9 days = 45/45 barn = 1 barn
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3 workers * 1/45 barn/day * x days = 1 barn
3 * 1/45 * x = 1
3/45*x = 1
3x = 45
x = 15 days
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Done.

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Another tutor has given you a good explanation of the team effort it takes for 5 men finishing the job in 9 days. Each man does 1%2F45 of the job per day. In that way, if the team consists of just 3 men, it takes that team 15 days to do the job.
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That being the case, for the extra credit part:
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If the job needs to be done in 7 days, each day the team of "x" number of men needs to do 1%2F7 of the job each day. Since each team member does 1%2F45 of the job in a day, if you multiply that times the unknown number of men, the answer must equal 1%2F7. In equation form this can be written as:
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%281%2F45%29%2Ax+=+1%2F7
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You can solve this equation for "x" by multiplying both sides of the equation by 45 as follows:
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45%2A%281%2F45%29%2Ax+=+45%281%2F7%29
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On the left side the multiplier of 45 cancels with the denominator and you are left with:
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x+=+45%2F7
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When you divide out the right side you get the answer 6+%26+3%2F7.
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Since 3%2F7 of a person is not realistic, 6 men will NOT complete the job in 7 days. Therefore, 7 men will complete the job before the end of the 7th day.
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Consider this ... 7 men, each doing 1%2F45 of the job per day will complete 7%2F45 of the job per day. Therefore, is 7 days they will do 7%2A%287%2F45%29 of the job. This tells you that in 7 days they will complete 49%2F45 of the job ... in other words the 7 man team in 7 days will have the capability to complete the 1 job and do a little more work on another job too.
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Hope this helps you score the extra credit.