SOLUTION: 4 men planned to complete a piece of work in 10 days,3 men worked for 4 days after which 4 men were employed.find the total number of days taken to complete the work?

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Question 1086672: 4 men planned to complete a piece of work in 10 days,3 men worked for 4 days after which 4 men were employed.find the total number of days taken to complete the work?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
4 men planned to complete a piece of work in 10 days
1 man will take 4 times as long to do the work
The rate for 1 man is [ 1 job ] / [ 40 days ]
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In 4 days 1 man does +4%2F40++=+1%2F10+ of the job
In 4 days 3 men do +3%2F10+ of the job
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There is +1+-+3%2F10+=+7%2F10+ of the job left to do
Let +t+ = time in days for 4 men to do +7%2F10+
of the job
One of the men will take 4 times as long to do +7%2F10+
of the job, so +%28%28+7%2F10+%29%29+%2F+%28%28+4t+%29%29+ is the rate for 1 man
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The rate for 1 man is [ 1 job ] / [ 40 days ], so I can say:
+1+%2F+40+=+%28%28+7%2F10+%29%29+%2F+%28%28+4t+%29%29+
+4t+=+40%2A%28+7%2F10+%29+
+t+=+10%2A%28+7%2F10+%29+
+t+=+7+ days
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The total nuber of days to complete the work is:
+4+%2B+7+=+11+ days
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Definitely get a 2nd opinion on this. I could easily
go off track on this.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
4 men planned to complete a piece of work in 10 days,3 men worked for 4 days after which 4 men were employed.find the total number of days taken to complete the work?
It depends!
In 4 days, 3 men completed: 3%2F10 of the job, leaving 7%2F10 undone.
Now, to complete the remaining 7%2F10 of the job, how many men are working? Is it:
1) the original 4, plus the newly-employed 4, for a total of 8?
2) the 3 that worked for 4 days, plus the 4 newly-employed 4, for a total of 7?
3) the 4 newly-employed for a total of 4?