document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=790028>Question 790028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Parallel processing uses two or more computers, working together, to solve a single problem. Using parallel processing, two computers can solve a problem in 6 minutes. If, working alone, one computer can solve a problem in 9 minutes less than the time needed by the second computer, how long would it take the faster computer working alone to solve the problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #479014 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=479014\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Let x = amount of time, in min the slower computer can do the task (on its own)\r<BR>\n" );
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document.write( "1/(x-9) + 1/x = 1/6\r<BR>\n" );
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document.write( "x/(x(x-9)) + (x-9)/(x(x-9)) = 1/6\r<BR>\n" );
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document.write( "(x + x-9)/(x(x-9)) = 1/6\r<BR>\n" );
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document.write( "(2x-9)/(x(x-9)) = 1/6\r<BR>\n" );
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document.write( "6(2x-9) = 1(x(x-9))\r<BR>\n" );
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document.write( "12x-54 = x^2-9x\r<BR>\n" );
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document.write( "0 = x^2-9x-12x+54\r<BR>\n" );
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document.write( "x^2-21x+54 = 0\r<BR>\n" );
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document.write( "(x-3)(x-18) = 0\r<BR>\n" );
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document.write( "x-3 = 0 or x-18 = 0\r<BR>\n" );
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document.write( "x = 3 or x = 18\r<BR>\n" );
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document.write( "Notice how if x = 3, then x-9 becomes 3-9 = -6. Since you can't have a negative time, this means that x = 3 is not allowed.\r<BR>\n" );
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document.write( "So x = 18 is the only allowed solution.\r<BR>\n" );
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document.write( "So it will take 18 minutes for the slower computer to do the job alone.\r<BR>\n" );
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document.write( "Therefore, it will take 18 - 9 = <font color=\"red\">9 minutes</font> for the faster computer to do the job alone.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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