SOLUTION: 55 men can finish a piece of work in 42 days. How many additional men must be added to complete the work 9 days earlier..?

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Question 1024283: 55 men can finish a piece of work in 42 days. How many additional men must be added to complete the work 9 days earlier..?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
1 man can finish the job in +55+ times that time
or: +55%2A42+=+2310+ days
This is: [ 1 job done ] / [ 2310 days ]
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Let +n+ = additional men to be added
1 man can do this job in +55+%2B+n+ times
the time it takes +55+%2B+n+ men
rate for 1 man = +1+%2F+%28%28+55+%2B+n+%29%2A%28+42+-+9+%29%29+
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These rates for 1 man are the same, so:
+1+%2F+2310+=+1+%2F+%28+%28+55+%2B+n+%29%2A33+%29+
+2310+=+%28+55+%2B+n+%29%2A33+
+2310+=+1815+%2B+33n+
+33n+=+495+
+n+=+15+
An additional 15 men are needed to
finish the job 9 days earlier
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check:
rate for 1 man is:
+1%2F2310+=+1%2F%28+%28+55+%2B+15+%29%2A33+%29+
+70%2A33++=+2310+
+2310+=+2310+
OK