document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=461620>Question 461620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cindy can paint a house in 3 hr less time than Dustin. Together, it takes 18 hrs. How long does it take each to do the job by theirselves?<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 #316539 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=316539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Cindy can paint a house in 3 hr less time than Dustin. Together, it takes 18 hrs. How long does it take each to do the job by theirselves?<BR>\n" );
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document.write( "Let x = time (hrs) it takes for Dustin<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x-3 = time it takes for Cindy<BR>\n" );
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document.write( "18(1/x + 1/(x-3)) = 1<BR>\n" );
document.write( "multiplying both sides by x(x-3):<BR>\n" );
document.write( "18((x-3) + x) = x(x-3)<BR>\n" );
document.write( "18(2x-3) = x^2-3x<BR>\n" );
document.write( "36x-54 = x^2-3x<BR>\n" );
document.write( "-54 = x^2-39x<BR>\n" );
document.write( "0 = x^2-39x+54<BR>\n" );
document.write( "solve by applying the \"quadratic formula\" to get:<BR>\n" );
document.write( "x = {37.56, 1.44}<BR>\n" );
document.write( "throw out the 1.44 (extraneous) to get<BR>\n" );
document.write( "x = 37.56 hours (Dustin)<BR>\n" );
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document.write( "Cindy<BR>\n" );
document.write( "x-3 = 37.56-3 = 34.56 hours<BR>\n" );
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document.write( "Details of quadratic follows:<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-39x%2B54+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-39x%2B54+=+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=%28-39%29%5E2-4%2A1%2A54=1305 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-39%29%5E2-4%2A1%2A54=1305\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1305 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--39%2B-sqrt%28+1305+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--39%2B-sqrt%28+1305+%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-%28-39%29%2Bsqrt%28+1305+%29%29%2F2%5C1+=+37.5623918681884 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-39%29%2Bsqrt%28+1305+%29%29%2F2%5C1+=+37.5623918681884\"   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-%28-39%29-sqrt%28+1305+%29%29%2F2%5C1+=+1.43760813181156 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-39%29-sqrt%28+1305+%29%29%2F2%5C1+=+1.43760813181156\"   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-39x%2B54 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-39x%2B54\"   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-39x%2B54+=+1%28x-37.5623918681884%29%2A%28x-1.43760813181156%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-39x%2B54+=+1%28x-37.5623918681884%29%2A%28x-1.43760813181156%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 37.5623918681884, 1.43760813181156.\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-39%2Ax%2B54+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-39%2Ax%2B54+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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