document.write( "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?\r
\n" ); document.write( "\n" ); document.write( "How do I write this problem into an equation and solve it
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Algebra.Com's Answer #612934 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
You can call the shed-building time [ t = hrs x days ]
\n" ); document.write( "since that gives you the total time, \"+t+\"
\n" ); document.write( "The rate of building 1 shed is:
\n" ); document.write( "[ 1 shed/t ]
\n" ); document.write( "\"+1%2Ft+=+1%2F%28+8%2A5%29+\"
\n" ); document.write( "\"+1%2F40+\"
\n" ); document.write( "-----------
\n" ); document.write( "Since this is the rate for \"+12+\" men, I
\n" ); document.write( "divide by \"+12+\" to get the rate for \"+1+\"
\n" ); document.write( "man to build 1 shed
\n" ); document.write( "\"+R+=+1%2F%28+40%2A12%29+=+1%2F480+\"
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\n" ); document.write( "\"+8+\" men will increase the rate to \"+8%2F480+=+1%2F60+\"
\n" ); document.write( "Let \"+d+\" = number of days \"+8+\" men take
\n" ); document.write( "\"+%28+1%2F60+%29%2A%28+10d+%29+=+1+\"
\n" ); document.write( "This is: [ rate ]x[ time ] = [ number of sheds ]
\n" ); document.write( "\"+d%2F6+=+1+\"
\n" ); document.write( "\"+d+=+6+\"
\n" ); document.write( "They take 6 days
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\n" ); document.write( "You can do it this way, too:
\n" ); document.write( "1/3 as many men take 3 times as long, so
\n" ); document.write( "4 men take 120 hrs
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\n" ); document.write( "Twice that many men take 1/2 as long, so
\n" ); document.write( "8 men take 60 hrs
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\n" ); document.write( "\"+60%2F10+=+6+\" days
\n" ); document.write( "This is [ hrs / ( hrs/day ) ] = [ days ]
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\n" ); document.write( "This isn't exactly an equation,
\n" ); document.write( "but I think it gives some insight
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