document.write( "Question 1009210: John and Bob can clean the house in 3 hours. If each work alone, it would take Bob one hour longer to clean the house than it would take John. How long would it take Bob to clean the house alone? \n" ); document.write( "
Algebra.Com's Answer #624799 by ptaylor(2198)\"\" \"About 
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Let x=amount of time it takes Bob to clean the house
\n" ); document.write( "Then Bob works at the rate of 1/x house per hour
\n" ); document.write( "John cleans the house in x-1 hours
\n" ); document.write( "So John cleans at the rate of 1/(x-1) house per hour
\n" ); document.write( "Together they clean at the rate of 1/3 house per hour
\n" ); document.write( "sooo
\n" ); document.write( "1/x +1/(x-1)= 1/3 multiply each term by 3x(x-1)
\n" ); document.write( "3(x-1)+3x=x(x-1)
\n" ); document.write( "3x-3+3x=x^2-x
\n" ); document.write( "x^2-7x+3=0
\n" ); document.write( "solve using quadratic formula and we get
\n" ); document.write( "x=~6.54 hrs and
\n" ); document.write( "x=~0.46 hrs---this cannot be correct. Can't have John cleaning in negative hours.
\n" ); document.write( "So the answer is x~=6.54 hours---time it takes Bob
\n" ); document.write( "Then 5.54 hours----time it takes John
\n" ); document.write( "CK
\n" ); document.write( "1/6.54 + 1/5.54 =1/3
\n" ); document.write( "0.1529 + 0.1805=0.3333
\n" ); document.write( "0.3334~~~~~0.3333\r
\n" ); document.write( "\n" ); document.write( "Hope this helps--ptaylor
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