document.write( "Question 65067: Karen and John take 3 hours to clean the house. Karen alone can clean the house 1 hour faster than John can clean the house alone. What is the total time it takes Karen to clean the house alone. \n" ); document.write( "
Algebra.Com's Answer #45585 by stanbon(75887)\"\" \"About 
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Karen and John take 3 hours to clean the house. Karen alone can clean the house 1 hour faster than John can clean the house alone. What is the total time it takes Karen to clean the house alone.
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\n" ); document.write( "Karen/John together DATA:
\n" ); document.write( "time=3 hrs/job; rate=(1/3)job/hr.
\n" ); document.write( "--------------------
\n" ); document.write( "John alone DATA:
\n" ); document.write( "time= x hrs/job; rate = (1/x)job/hr.
\n" ); document.write( "--------------------
\n" ); document.write( "Karen alone DATA:
\n" ); document.write( "time = (x+1) hr/job ; rate = 1/(x+1) job/hr
\n" ); document.write( "--------
\n" ); document.write( "EQUATION:
\n" ); document.write( "rate + rate = rate together
\n" ); document.write( "(1/x)+1/(x+1)= 1/3
\n" ); document.write( "Multiply thru by 3x(x+1) to get:
\n" ); document.write( "3(x+1)+3x = x(x+1)
\n" ); document.write( "6x+3=x^2+x
\n" ); document.write( "x^2-5x-3=0
\n" ); document.write( "x=[5+-sqrt(25-4*-3)]/2
\n" ); document.write( "x=[5+-sqrt(37)]/2
\n" ); document.write( "x= 5.541 hrs
\n" ); document.write( "x+1=6.541 hrs (Time it takes Karen alone to clean the house)
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
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