document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471037>Question 471037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 83 miles at a certain speed. The canoeist travels 6 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hours. What was the  on each part of the trip?<BR>\n" );
document.write( "The speed of the first part of the trip was ___mph.<BR>\n" );
document.write( "(Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth.)<BR>\n" );
document.write( "The speed of the second part of the trip was __ mph.<BR>\n" );
document.write( "(Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323106 by </B><A HREF=/tutors/aboutme.mpl?userid=jorel1380><B>jorel1380(3719)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jorel1380><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=jorel1380><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=323106\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 83/(n+5)+6/n=2<BR>\n" );
document.write( "83n+6n+30=2n2+10n<BR>\n" );
document.write( "2n2-79n+30=0<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=2x%5E2%2B-79x%2B30+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-79x%2B30+=+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=%28-79%29%5E2-4%2A2%2A30=6001 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-79%29%5E2-4%2A2%2A30=6001\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=6001 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--79%2B-sqrt%28+6001+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--79%2B-sqrt%28+6001+%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-%28-79%29%2Bsqrt%28+6001+%29%29%2F2%5C2+=+39.1165304068643 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-79%29%2Bsqrt%28+6001+%29%29%2F2%5C2+=+39.1165304068643\"   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-%28-79%29-sqrt%28+6001+%29%29%2F2%5C2+=+0.383469593135686 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-79%29-sqrt%28+6001+%29%29%2F2%5C2+=+0.383469593135686\"   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=2x%5E2%2B-79x%2B30 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-79x%2B30\"   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=2x%5E2%2B-79x%2B30+=+2%28x-39.1165304068643%29%2A%28x-0.383469593135686%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-79x%2B30+=+2%28x-39.1165304068643%29%2A%28x-0.383469593135686%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 39.1165304068643, 0.383469593135686.\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+2%2Ax%5E2%2B-79%2Ax%2B30+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-79%2Ax%2B30+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "The answer is 39.1165304068643 mph or 0.383469593135686 mph.  Throwing out the second answer as impractical, we get the speed going as 44.1165304068643 mph, and the speed going back as 39.1165304068643 mph.. </SPAN>\n" );
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