Question 520556
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 {{{1/45}}} 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 {{{1/7}}} of the job each day. Since each team member does {{{1/45}}} of the job in a day, if you multiply that times the unknown number of men, the answer must equal {{{1/7}}}. In equation form this can be written as:
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{{{(1/45)*x = 1/7}}}
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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*(1/45)*x = 45(1/7)}}}
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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 = 45/7}}}
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When you divide out the right side you get the answer {{{6 & 3/7}}}.
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Since {{{3/7}}} 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 {{{1/45}}} of the job per day will complete {{{7/45}}} of the job per day. Therefore, is 7 days they will do {{{7*(7/45)}}} of the job. This tells you that in 7 days they will complete {{{49/45}}} 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.