document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206942>Question 206942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two technicians can complete a mailing in 3 hours when working together. alone, one can complete the mailing 2 hours faster than the other. how long will it take each person to complete the mailing alone? compute answer to two decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156439 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=156439\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     two technicians can complete a mailing in 3 hours when working together. alone, one can complete the mailing 2 hours faster than the other. how long will it take each person to complete the mailing alone? compute answer to two decimal places.<BR>\n" );
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document.write( "Let x = time it takes to complete mailing by slower tech<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x-2 = time it takes by faster tech<BR>\n" );
document.write( ".<BR>\n" );
document.write( "3(1/x + 1/(x-2)) = 1<BR>\n" );
document.write( "3/x + 3/(x-2) = 1<BR>\n" );
document.write( "Multiply both sides by a common denominator x(x-2):<BR>\n" );
document.write( "3(x-2) + 3x = x(x-2)<BR>\n" );
document.write( "3x-6 + 3x = x^2-2x<BR>\n" );
document.write( "6x-6 = x^2-2x<BR>\n" );
document.write( "-6 = x^2-8x<BR>\n" );
document.write( "0 = x^2-8x+6<BR>\n" );
document.write( "Solve using the quadratic equation yields:<BR>\n" );
document.write( "x = {7.16, 0.84}<BR>\n" );
document.write( "We can throw out the 0.84 solution because it will give a negative answer for the faster tech leaving us with:<BR>\n" );
document.write( "x = 7.16 hours for the slower tech<BR>\n" );
document.write( "x-2 = 7.16-2 = 5.16 hours for the faster tech<BR>\n" );
document.write( ".<BR>\n" );
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-8x%2B6+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-8x%2B6+=+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=%28-8%29%5E2-4%2A1%2A6=40 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-8%29%5E2-4%2A1%2A6=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=40 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--8%2B-sqrt%28+40+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--8%2B-sqrt%28+40+%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-%28-8%29%2Bsqrt%28+40+%29%29%2F2%5C1+=+7.16227766016838 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+40+%29%29%2F2%5C1+=+7.16227766016838\"   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-%28-8%29-sqrt%28+40+%29%29%2F2%5C1+=+0.83772233983162 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-8%29-sqrt%28+40+%29%29%2F2%5C1+=+0.83772233983162\"   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-8x%2B6 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-8x%2B6\"   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-8x%2B6+=+1%28x-7.16227766016838%29%2A%28x-0.83772233983162%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-8x%2B6+=+1%28x-7.16227766016838%29%2A%28x-0.83772233983162%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 7.16227766016838, 0.83772233983162.\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-8%2Ax%2B6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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