SOLUTION: Certain men can complete a work in 160 days .If there were 10 men more,the work would have been complete in 20 days less.How many men were there?

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Question 975774: Certain men can complete a work in 160 days .If there were 10 men more,the work would have been complete in 20 days less.How many men were there?
Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
n, certain quantity of men to do work.
nr, the rate for n men to do work.

nr%2A160=1, one job complete.

Ten more men:
%28n%2B10%29r%28160-20%29=1
%28n%2B10%29r%28140%29=1
140nr%2B1400r=1

System of Equations:
system%28nr%2A160=1%2C140nr%2B1400r=1%29

You can solve and substitute for nr, first to find r.

nr=1%2F160
;
140%281%2F160%29%2B1400r=1
14%2F16%2B1400r=1
1400r=1-7%2F8
1400r=1%2F8
highlight_green%28r=1%2F%288%2A1400%29%29-----now the rate of one man is known.

Return to the first equation, nr%2A160=1.
Solve for n, how many men.
-
n=1%2F%28160r%29
n=1%2F%28160%2F%288%2A1400%29%29
n=1%2F%2816%2F%288%2A140%29%29
n=1%2F%282%2F140%29=140%2F2
highlight%28n=70%29