document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33180>Question 33180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Working alone, Steve can paint a house in 2 hours less than Gary. Working together, they can paint a house in 10 hours. How long would it take Gary to paint the house 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 #19590 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=19590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Steve Data:<BR>\n" );
document.write( " time=x-2 hrs/job  rate = 1/(x-2) job/hr<BR>\n" );
document.write( "Gary Data:<BR>\n" );
document.write( " time= x hrs/job   rate= 1/x job/hr<BR>\n" );
document.write( "Working together Data:<BR>\n" );
document.write( " time= 10 hrs/job  rate=1/10 job/hr.<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "rate + rate = 1/10<BR>\n" );
document.write( "1/(x-2) + 1/x = 1/10<BR>\n" );
document.write( "10x +10(x-2)= x(x-2)<BR>\n" );
document.write( "20x-20 = x^2-2x<BR>\n" );
document.write( "x^2-22x+20=0<BR>\n" );
document.write( "<TABLE  BORDER=1>\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-22x%2B20+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-22x%2B20+=+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=%28-22%29%5E2-4%2A1%2A20=404 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-22%29%5E2-4%2A1%2A20=404\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=404 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--22%2B-sqrt%28+404+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--22%2B-sqrt%28+404+%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-%28-22%29%2Bsqrt%28+404+%29%29%2F2%5C1+=+21.0498756211209 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-22%29%2Bsqrt%28+404+%29%29%2F2%5C1+=+21.0498756211209\"   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-%28-22%29-sqrt%28+404+%29%29%2F2%5C1+=+0.95012437887911 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-22%29-sqrt%28+404+%29%29%2F2%5C1+=+0.95012437887911\"   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-22x%2B20 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-22x%2B20\"   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-22x%2B20+=+1%28x-21.0498756211209%29%2A%28x-0.95012437887911%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-22x%2B20+=+1%28x-21.0498756211209%29%2A%28x-0.95012437887911%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 21.0498756211209, 0.95012437887911.\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-22%2Ax%2B20+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-22%2Ax%2B20+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "From this you see x=21.05 hrs (amount of time Gary requires to do the job alone. It can't be x=0.95 for then Steve's time(x-2) would be negative.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );