document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987576>Question 987576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A and B working together can do a job in 10 days. One takes 5 days less than the other to do the job when each works alone. How many days would it take each of them working alone to do the job?\r<BR>\n" );
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document.write( "P.S.: My math teacher said that the answer to this question is radicals<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #608307 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=608307\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets assume a can do 1/A of the job in a day. and B can do 1/B of the job in a day.\r<BR>\n" );
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document.write( "You are told<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+10%2A%28%281%2FA%29+%2B+%281%2FB%29%29 ALIGN=MIDDLE  ALT=\"1+=+10%2A%28%281%2FA%29+%2B+%281%2FB%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1+=+%28B%2BA%29%2FAB ALIGN=MIDDLE  ALT=\"0.1+=+%28B%2BA%29%2FAB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1AB+=+B%2BA ALIGN=MIDDLE  ALT=\"0.1AB+=+B%2BA\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You are also told that A can do the job in X days. B takes X+5 days\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+%281%2FA%29X ALIGN=MIDDLE  ALT=\"1+=+%281%2FA%29X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=X ALIGN=MIDDLE  ALT=\"A=X\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+%281%2FB%29%28X%2B5%29 ALIGN=MIDDLE  ALT=\"1+=+%281%2FB%29%28X%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+X%2B5 ALIGN=MIDDLE  ALT=\"B+=+X%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug those values for A and B into the equation above\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1%28X%29%28X%2B5%29+=+X+%2B+%28X%2B5%29 ALIGN=MIDDLE  ALT=\"0.1%28X%29%28X%2B5%29+=+X+%2B+%28X%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1X%5E2+%2B+0.5X+=+2X+%2B+5 ALIGN=MIDDLE  ALT=\"0.1X%5E2+%2B+0.5X+=+2X+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1X%5E2+-1.5X+-+5+=+0 ALIGN=MIDDLE  ALT=\"0.1X%5E2+-1.5X+-+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=0.1x%5E2%2B-1.5x%2B-5+=+0 ALIGN=MIDDLE  ALT=\"0.1x%5E2%2B-1.5x%2B-5+=+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=%28-1.5%29%5E2-4%2A0.1%2A-5=4.25 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1.5%29%5E2-4%2A0.1%2A-5=4.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4.25 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--1.5%2B-sqrt%28+4.25+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--1.5%2B-sqrt%28+4.25+%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-%28-1.5%29%2Bsqrt%28+4.25+%29%29%2F2%5C0.1+=+17.8077640640442 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-1.5%29%2Bsqrt%28+4.25+%29%29%2F2%5C0.1+=+17.8077640640442\"   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-%28-1.5%29-sqrt%28+4.25+%29%29%2F2%5C0.1+=+-2.80776406404415 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-1.5%29-sqrt%28+4.25+%29%29%2F2%5C0.1+=+-2.80776406404415\"   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=0.1x%5E2%2B-1.5x%2B-5 ALIGN=MIDDLE  ALT=\"0.1x%5E2%2B-1.5x%2B-5\"   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=0.1x%5E2%2B-1.5x%2B-5+=+0.1%28x-17.8077640640442%29%2A%28x--2.80776406404415%29 ALIGN=MIDDLE  ALT=\"0.1x%5E2%2B-1.5x%2B-5+=+0.1%28x-17.8077640640442%29%2A%28x--2.80776406404415%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 17.8077640640442, -2.80776406404415.\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+0.1%2Ax%5E2%2B-1.5%2Ax%2B-5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.1%2Ax%5E2%2B-1.5%2Ax%2B-5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "so A take 17.8 days and B takes 22.8 days by themselves </SPAN>\n" );
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