document.write( "Question 248629: One maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone? \n" ); document.write( "

Algebra.Com's Answer #181169 by josmiceli(19441) $\"\"$ $\"About$

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Faster maid's rate of working + slower maids rate = rate working together
\n" ); document.write( "Let $\"x\"$ = slower maids rate of working in (1 house cleaned)/(time to clean it)
\n" ); document.write( "then, Faster maid's rate = $\"3x\"$
\n" ); document.write( " $\"x+%2B+3x+=+1%2F3\"$ (note: 1/3 is: (1 house/(3 hours))
\n" ); document.write( " $\"3x+%2B+9x+=+1\"$
\n" ); document.write( " $\"12x+=+1\"$
\n" ); document.write( " $\"x+=+1%2F12\"$
\n" ); document.write( "The slower maid can clean 1 house in 12 hours
\n" ); document.write( "The faster maid's rate is:
\n" ); document.write( " $\"3x+=+3%2A%281%2F12%29+=+3%2F12\"$
\n" ); document.write( " $\"3%2F12+=+1%2F4\"$
\n" ); document.write( "The faster maid can clean the house in 4 hours \n" ); document.write( "

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