document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997068>Question 997068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jerry can lay a tile floor in 3 hours less time than Jake. If they can work together, the floor takes 2 hours. How long would it take Jerry to lay the floor by himself? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615320 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = quantity of work.\r<BR>\n" );
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document.write( "quantity of work = 1 job\r<BR>\n" );
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document.write( "jerry can lay a tile floor in 3 hours less time than jake.\r<BR>\n" );
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document.write( "let x = the amount of time that jake takes.<BR>\n" );
document.write( "then x - 3 = the amount of time that jerry takes.\r<BR>\n" );
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document.write( "since rate * time = quantity, then:\r<BR>\n" );
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document.write( "for jake, rate * time = quantity becomes rate * x = 1\r<BR>\n" );
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document.write( "for jerry, rate * time = quantity becomes rate * (x-3) = 1\r<BR>\n" );
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document.write( "solve for rate in each of these equations and you get:\r<BR>\n" );
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document.write( "for jake, rate = 1/x\r<BR>\n" );
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document.write( "for jerry, rate = 1/(x-3)\r<BR>\n" );
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document.write( "when they work together, they can do the job in 2 hours.\r<BR>\n" );
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document.write( "their rates are additive when they work together.\r<BR>\n" );
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document.write( "time is equal to 2 hours.<BR>\n" );
document.write( "quanity is still equal to 1 job.\r<BR>\n" );
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document.write( "rate * time = quantity becomes:\r<BR>\n" );
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document.write( "(1/x + 1/(x-3) * 2 = 1\r<BR>\n" );
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document.write( "you want to solve for x.\r<BR>\n" );
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document.write( "remove the parentheses to get:\r<BR>\n" );
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document.write( "2/x + 2/(x-3) = 1\r<BR>\n" );
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document.write( "multiply both sides of the equation by x * (x-3) to get:\r<BR>\n" );
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document.write( "(2 * x * (x-3) / x + (2 * x * (x-3)) / (x-3) = 1 * x * (x-3)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "2 * (x-3) + 2 * x = x * (x-3)\r<BR>\n" );
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document.write( "remove parentheses to get:\r<BR>\n" );
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document.write( "2 * x - 6 + 2 * x = x^2 - 3 * x\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "4 * x - 6 = x^2 - 3 * x\r<BR>\n" );
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document.write( "subtract 4 * x from both sides of the equation and add 6 to both sides of the equation to get:\r<BR>\n" );
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document.write( "0 = x^2 - 7 * x + 6\r<BR>\n" );
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document.write( "solve for the factors of this quadratic equation to get:\r<BR>\n" );
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document.write( "(x - 6) * (x - 1) = 0\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 6 or x = 1\r<BR>\n" );
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document.write( "x can't be equal to 1 because then x - 3 would be negative and negative values of time or rate are not allowed.\r<BR>\n" );
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document.write( "x has to be equal to 6 or not at all.\r<BR>\n" );
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document.write( "to confirm that x = 6 is good, go back to the original equation where they were both working together to get:\r<BR>\n" );
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document.write( "(1/x + 1/(x-3) * 2 = 1 becomes:\r<BR>\n" );
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document.write( "(1/6 + 1/(6-3)) * 2 = 1 which becomes:\r<BR>\n" );
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document.write( "(1/6 + 1/3) * 2 = 1 which becomes:\r<BR>\n" );
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document.write( "(1/6 + 2/6) * 2 = 1 which becomes:\r<BR>\n" );
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document.write( "3/6 * 2 = 1 which is equal to 1/2 * 2 = 1 which is equal to 1 = 1.\r<BR>\n" );
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document.write( "this confirms the value of x is good.\r<BR>\n" );
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document.write( "you are asked how long it would take jerry working alone.\r<BR>\n" );
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document.write( "rate * time = quantity\r<BR>\n" );
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document.write( "quantity = 1<BR>\n" );
document.write( "rate = 1/(6-3) = 1/3\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "1/3 * time = 1\r<BR>\n" );
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document.write( "solve for time to get time = 3 hours.\r<BR>\n" );
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document.write( "it would take jerry 3 hours to do the job working alone.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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