SOLUTION: Four men working together can dig a trench in 42 days. They begin the job, but one worker works only 1/2 days. How long will it take to complete the job?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Four men working together can dig a trench in 42 days. They begin the job, but one worker works only 1/2 days. How long will it take to complete the job?      Log On


   

Question 831014: Four men working together can dig a trench in 42 days. They begin the job, but one worker works only 1/2 days. How long will it take to complete the job?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate for 4 men is 1 trench in 42 days
Let +x+ = the fraction of a trench dug
by 4 men in 1/2 day
+1%2F42+%2B+x%2F%28%281%2F2%29%29+
+1%2F42+=+2x+
+x+=+1%2F84+
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That means there is +1+-+1%2F84+=+83%2F84+
of a trench left to dig after 1/2 day
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3 men have to finish the job
If 4 men take 42 days to dig a trench,
1 man takes 4 times as long, or +4%2A42+=+168+ days
3 men take 1/3 of that time, or 56 days
Let y = the number of days for 3
men to dig +83%2F84+ of the trench
+1%2F56+=+%28+83%2F84%29%2Fy+
+y%2A%28+1%2F56+%29+=+83%2F84+
+y+=+%28+56%2A83%29+%2F+84+
+y+=+4648%2F84+
+y+=+55.333+
It will take +.5+%2B+55.333+=+55.5333+ days
to finish the job
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Hope I got it