document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=312525>Question 312525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #223451 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=223451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?<BR>\n" );
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document.write( "Let x = days it taks Ron to frame it alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x-4 = days it takes Lee to frame it alone<BR>\n" );
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document.write( "4(1/x + 1/(x-4)) = 1<BR>\n" );
document.write( "multiplying both sides by x(x-4):<BR>\n" );
document.write( "4((x-4) + x) = x(x-4)<BR>\n" );
document.write( "4(2x-4) = x(x-4)<BR>\n" );
document.write( "8x-8 = x^2-4x<BR>\n" );
document.write( "-8 = x^2-12x<BR>\n" );
document.write( "0 = x^2-12x+8<BR>\n" );
document.write( "x = {11.292, 0.708}<BR>\n" );
document.write( "Tossing out the 0.708 (because it won't make sense) leaves us with:<BR>\n" );
document.write( "x = 11.292 days (Time it takes Ron)<BR>\n" );
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document.write( "Lee:<BR>\n" );
document.write( "x-4 = 11.292-4 = 7.292 days <BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-12x%2B8+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-12x%2B8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-12%29%5E2-4%2A1%2A8=112 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-12%29%5E2-4%2A1%2A8=112\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=112 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--12%2B-sqrt%28+112+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--12%2B-sqrt%28+112+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+112+%29%29%2F2%5C1+=+11.2915026221292 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+112+%29%29%2F2%5C1+=+11.2915026221292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-12%29-sqrt%28+112+%29%29%2F2%5C1+=+0.708497377870819 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-12%29-sqrt%28+112+%29%29%2F2%5C1+=+0.708497377870819\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-12x%2B8 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-12x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-12x%2B8+=+1%28x-11.2915026221292%29%2A%28x-0.708497377870819%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-12x%2B8+=+1%28x-11.2915026221292%29%2A%28x-0.708497377870819%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 11.2915026221292, 0.708497377870819.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B8+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B8+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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