document.write( "Question 1185232: Joe can paint a room in 6 hours less time than Jay. If they can paint the
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Algebra.Com's Answer #816026 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Joe can paint a room in 6 hours less time than Jay. If they can paint the
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document.write( "Let x be the time for Joe to complete the job alone, in hours;\r\n" );
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document.write( "then the time for Jay is (x+6) hours.\r\n" );
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document.write( "In one hour, Joe makes    part of the entire job, working alone;\r\n" );
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document.write( "             Jay makes    part of the entire job, working alone.\r\n" );
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document.write( "Working together, they make    of the job in one hour.\r\n" );
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document.write( "It gives an equation\r\n" );
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document.write( "     +  = .       (1)\r\n" );
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document.write( "It is your basic equation.  As soon as you get it, the setup is done.\r\n" );
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document.write( "To solve the equation, multiply both sides by  4x*(x+6)  and simplfy.   You will get\r\n" );
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document.write( "    4(x+6) + 4x = x^2 + 6x\r\n" );
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document.write( "    x^2 - 2x - 24 = 0.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (x-6)*(x+4) = 0.\r\n" );
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document.write( "Of two roots,  x= 6  and  x= 4, only positive x= 6 is meaningful.\r\n" );
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document.write( "It gives the ANSWER to the problem:\r\n" );
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document.write( "    Joe con make the entire work in 6 hours, working alone;  Jay can do it in 6+6 = 12 hours.\r\n" );
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document.write( "CHECK.    +  =  =  =  = .   !  Correct.  Equation (1)  is held  !\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a standard and 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 lesson\r
\n" ); document.write( "\n" ); document.write( " - Using quadratic equations to solve word problems on joint work \r
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\n" ); document.write( "\n" ); document.write( "Read it 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
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this textbook under the topic
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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