document.write( "Question 829618: Betty can mop the floor in 8 minutes. Together Betty and Nancy can mop the floor in just 6 minutes. How long does it take Nancy to mop the floor alone? \r
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Algebra.Com's Answer #499979 by LinnW(1048) $\"\"$ $\"About$

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b = Betty's rate in floors per minute is 1 floor/8 min = 1/8 floor per minute.
\n" ); document.write( "n = Nancy's rate
\n" ); document.write( "(b+n)6 = 1 floor
\n" ); document.write( "( 1/8 + n )6 = 1
\n" ); document.write( " 6/8 + 6n = 1
\n" ); document.write( "subtract 6/8 from each side
\n" ); document.write( " 6n = 1 - 6/8
\n" ); document.write( " 6n = 8/8 -6/8
\n" ); document.write( " 6n = 2/8
\n" ); document.write( "multiply each side by 1/6
\n" ); document.write( " n = (1/6)(2/8)
\n" ); document.write( " = 2/48
\n" ); document.write( " = 1/24
\n" ); document.write( "Let's check
\n" ); document.write( "(1/8 + 1/24)6 ?= 1
\n" ); document.write( "(3/24 + 1/24)6 ?= 1
\n" ); document.write( "(4/24)6 ?= 1
\n" ); document.write( "(1/6)(6) = 1
\n" ); document.write( "So it checks out.
\n" ); document.write( "Nancy's rate is 1/24 floor per minute, so she will need 24 minutes to mop
\n" ); document.write( "the floor. \n" ); document.write( "

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