document.write( "Question 1089560: A father and his son can clean the house together in 8 hours. When the son works alone, it takes him an hour longer to clean than it takes his dad alone. Find how long it takes the son to clean alone. \n" ); document.write( "

Algebra.Com's Answer #703895 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let x be the time in hours for son to complete the job working alone.\r\n" );
document.write( "Then the time for the father is x-1 hours.\r\n" );
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document.write( "The son's    rate of work is        of the job per hour.\r\n" );
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document.write( "The father's rate of work is    of the job per hour.\r\n" );
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document.write( "Their combined rate of work is  .\r\n" );
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document.write( "From the other side, the condition says that their combined rate of work is    of the job per hour.\r\n" );
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document.write( "It gives you an equation \r\n" );
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document.write( " = .\r\n" );
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document.write( "To solve it, multiply both sides by 8x*(x-1). You will get\r\n" );
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document.write( "8(x-1) + 8x = x*(x-1).\r\n" );
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document.write( "Simplify and solve for x:\r\n" );
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document.write( "x^2 - 17x + 8 = 0,\r\n" );
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document.write( " =  =  = .\r\n" );
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document.write( "Only positive root works: x =  = 16.5 hours = 16 hours and 30 minutes (approximately).\r\n" );
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document.write( "Check.   = 0.1251;    = 0.125.\r\n" );
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document.write( "               Check is good !.\r\n" );
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document.write( "Answer.  It will take approximately 16.5 hours for the son to make this job working alone.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "It is a typical joint work problem.\r
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\n" ); document.write( "\n" ); document.write( "There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Using Fractions to solve word problems on joint work \r
\n" ); document.write( "\n" ); document.write( "    - Solving more complicated word problems on joint work \r
\n" ); document.write( "\n" ); document.write( "    - Selected joint-work word problems from the archive \r
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\n" ); document.write( "\n" ); document.write( "Read them and get be trained in solving joint-work problems.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic
\n" ); document.write( "\"Rate of work and joint work problems\" of the section \"Word problems\".\r
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