document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=730880>Question 730880</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jake can cut and split a cord of firewood in 6 fewer hours than Steve.  When they work together, it takes them 4 hours.  How long would it take each of them to do the job alone?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446892 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=446892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let \r<BR>\n" );
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document.write( "x = number of hours it takes Jake to do the job if he worked alone\r<BR>\n" );
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document.write( "y = number of hours it takes Steve to do the job if he worked alone\r<BR>\n" );
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document.write( "We are told that \"Jake can cut and split a cord of firewood in 6 fewer hours than Steve\", so\r<BR>\n" );
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document.write( "x = y - 6\r<BR>\n" );
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document.write( "\"When they work together, it takes them 4 hours\", we can construct this equation\r<BR>\n" );
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document.write( "1/x + 1/y = 1/4\r<BR>\n" );
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document.write( "4xy(1/x) + 4xy(1/y) = 4xy(1/4) ... multiply EVERY term by the LCD 4xy to clear out the fractions\r<BR>\n" );
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document.write( "4y + 4x = xy\r<BR>\n" );
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document.write( "4y + 4(y-6) = (y-6)y ... plug in x = y-6\r<BR>\n" );
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document.write( "4y + 4(y-6) = (y-6)y\r<BR>\n" );
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document.write( "4y + 4y - 24 = y^2-6y\r<BR>\n" );
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document.write( "8y - 24 = y^2-6y\r<BR>\n" );
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document.write( "0 = y^2-6y-8y+24\r<BR>\n" );
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document.write( "0 = y^2-14y+24\r<BR>\n" );
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document.write( "y^2-14y+24 = 0\r<BR>\n" );
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document.write( "(y-12)(y-2) = 0\r<BR>\n" );
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document.write( "y-12 = 0 or y-2 = 0\r<BR>\n" );
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document.write( "y = 12 or y = 2\r<BR>\n" );
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document.write( "So the possible solutions for y are\r<BR>\n" );
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document.write( "y = 12 or y = 2\r<BR>\n" );
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document.write( "If y = 2, then \r<BR>\n" );
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document.write( "x = y - 6\r<BR>\n" );
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document.write( "x = 2 - 6\r<BR>\n" );
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document.write( "x = -4\r<BR>\n" );
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document.write( "So y CANNOT be 2 because this makes x a negative number.\r<BR>\n" );
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document.write( "So toss out y = 2 as a solution\r<BR>\n" );
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document.write( "If y = 12, then\r<BR>\n" );
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document.write( "x = y - 6\r<BR>\n" );
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document.write( "x = 12 - 6\r<BR>\n" );
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document.write( "x = 6\r<BR>\n" );
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document.write( "So if y = 12, then x = 6\r<BR>\n" );
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document.write( "Therefore, \r<BR>\n" );
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document.write( "Jake can do the job in <font color=\"red\">6 hours</font> if he worked alone. \r<BR>\n" );
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document.write( "Steve can do the job in <font color=\"red\">12 hours</font> if he worked alone. </SPAN>\n" );
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