document.write( "Question 996949: working along henry takes 9 hours longer than mary to clean the carpets in the entire office working together they clean the carpets in 6 hours how long wound it take mary to clean the office carpets if henry were not there to help? \n" ); document.write( "
Algebra.Com's Answer #615223 by josmiceli(19441)\"\" \"About 
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Add their rates of working to get
\n" ); document.write( "their rate working together
\n" ); document.write( "Let \"+t+\" = Mary's time to clean the carpets
\n" ); document.write( "------------------
\n" ); document.write( "Mary's rate working alone:
\n" ); document.write( "[ 1 office ] / [ t hrs ]
\n" ); document.write( "Henry's rate:
\n" ); document.write( "[ 1 office ] / [ t + 9 hrs ]
\n" ); document.write( "Working together:
\n" ); document.write( "[ 1 ofice ] / [ 6 hrs ]
\n" ); document.write( "---------------------
\n" ); document.write( "\"+1%2Ft+%2B+1%2F%28+t%2B9+%29+=+1%2F6+\"
\n" ); document.write( "Multiply both sides by \"+6t%2A%28+t%2B9+%29+\"
\n" ); document.write( "\"+6%2A%28+t%2B9+%29+%2B+6t+=+t%2A%28+t%2B9+%29+\"
\n" ); document.write( "\"+6t+%2B+54+%2B+6t+=+t%5E2+%2B+9t+\"
\n" ); document.write( "\"+t%5E2+-+3t+-+54+=+0+\"
\n" ); document.write( "\"+%28+t+-+9+%29%2A%28+t+%2B+6+%29+=+0+\" ( by looking at it )
\n" ); document.write( "\"+t+=+9+\" ( can't use negative time )
\n" ); document.write( "It takes Mary 9 hrs working alone
\n" ); document.write( "----------
\n" ); document.write( "check:
\n" ); document.write( "\"+1%2Ft+%2B+1%2F%28+t%2B9+%29+=+1%2F6+\"
\n" ); document.write( "\"+1%2F9+%2B+1%2F%289%2B9+%29+=+1%2F6+\"
\n" ); document.write( "\"+2%2F18+%2B+1%2F18+=+3%2F18+\"
\n" ); document.write( "\"+3%2F18+=+3%2F18+\"
\n" ); document.write( "OK \n" ); document.write( "
\n" );