SOLUTION: If 12 men working 8 hours a day can construct a shed in 5 days, then in how many days will 8 men working 10 hours a day complete the same job? How do I write this problem into a

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If 12 men working 8 hours a day can construct a shed in 5 days, then in how many days will 8 men working 10 hours a day complete the same job? How do I write this problem into a      Log On


   

Question 993707: If 12 men working 8 hours a day can construct a shed in 5 days, then in how many days will 8 men working 10 hours a day complete the same job?
How do I write this problem into an equation and solve it
Found 2 solutions by LinnW, josmiceli:
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
12 men working (8 * 5) hours complete the job.
12 men working 40 hours to complete.
12* 40 = 480 man hours to complete.
480/(8 * 10) = days to complete, that is 480 man hours divided by man hours per day
480 /80 = 6 days to complete

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can call the shed-building time [ t = hrs x days ]
since that gives you the total time, +t+
The rate of building 1 shed is:
[ 1 shed/t ]
+1%2Ft+=+1%2F%28+8%2A5%29+
+1%2F40+
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Since this is the rate for +12+ men, I
divide by +12+ to get the rate for +1+
man to build 1 shed
+R+=+1%2F%28+40%2A12%29+=+1%2F480+
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+8+ men will increase the rate to +8%2F480+=+1%2F60+
Let +d+ = number of days +8+ men take
+%28+1%2F60+%29%2A%28+10d+%29+=+1+
This is: [ rate ]x[ time ] = [ number of sheds ]
+d%2F6+=+1+
+d+=+6+
They take 6 days
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You can do it this way, too:
1/3 as many men take 3 times as long, so
4 men take 120 hrs
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Twice that many men take 1/2 as long, so
8 men take 60 hrs
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+60%2F10+=+6+ days
This is [ hrs / ( hrs/day ) ] = [ days ]
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This isn't exactly an equation,
but I think it gives some insight