SOLUTION: A crew of ten workers was hired to complete a job in 8 days. After working for two days, there was a new request to complete this job in two days. How many more workers need to be

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A crew of ten workers was hired to complete a job in 8 days. After working for two days, there was a new request to complete this job in two days. How many more workers need to be       Log On


   

Question 1067620: A crew of ten workers was hired to complete a job in 8 days. After working for two days, there was a new request to complete this job in two days. How many more workers need to be hired to finish this job in 2 days?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the 10 workers, working at
their normal rate would finish the job in exactly
8 days.
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The rate of working for 1 worker is:
[ 1/10 of the job ] / [ 8 days ] = [ 1 job ] / [ 80 days ]
This is also [ 1/80 of the job ] / [ 1 day ]
In 2 days, the fraction of the job that gets done is:
+2%2A%28+1%2F80+%29+=+1%2F40+
The leaves +39%2F40+ of the job left
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Now the rate has to be +%28+39%2F40+%29+%2F+2+=+39%2F80+ jobs/days
Let +n+ = the number of additional workers needed to
finish the job in 2 days
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+%28+10+%2B+n+%29%2A%28+1%2F80+%29+=+39%2F80+
Multiply both sides by +80+
+10+%2B+n+=+39+
+n+=+29+
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29 additional workers need to be added
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check answer: there is a total of +39+ workers to
do 39/40 of the job in +2+ days
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Each worker will do +%281%2F39%29%2A%2839%2F40%29+=+1%2F40+ of the job in +2+ days
That is +1%2F80+ of the job in 1 day
This agrees with my original calculation
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Definitely try to get another opinion on this!






Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A crew of ten workers was hired to complete a job in 8 days. After working for two days, there was a new request to complete this job in two days. How many more workers need to be hired to finish this job in 2 days?
Fraction of job done by 10 workers in 2 days: 1%2F4  

Fraction of job remaining after 10 workers worked 2 days: matrix%281%2C3%2C+1+-+1%2F4%2C+or%2C+3%2F4%29

Now, 3%2F4 of job remains to be done in 2 days, by 10 + A, with A being the additional workers

This will take: highlight_green%28matrix%281%2C3%2C+20%2C+additional%2C+workers%29%29, or a total of 30 (10 + 20) workers to complete the job in 2 days.