document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034960>Question 1034960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sandy made a trip to a city 200 miles away and then returned home. Her average speed on the return trip was 10 mph less than her average speed going. If her total travel time was 9 hours, what was her average rate in each direction? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649621 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=649621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sandy made a trip to a city 200 miles away and then returned home. Her average speed on the return trip was 10 mph less than her average speed going. If her total travel time was 9 hours, what was her average rate in each direction?<BR>\n" );
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document.write( "r = speed going<BR>\n" );
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document.write( "d = r*t<BR>\n" );
document.write( "t = d/r<BR>\n" );
document.write( "200/r + 200/(r-10) = 9<BR>\n" );
document.write( "200(r-10) + 200r = 9r(r-10)<BR>\n" );
document.write( "400r - 2000 = 9r^2 - 90r<BR>\n" );
document.write( "9r^2 - 490r + 1910  = 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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=9x%5E2%2B-490x%2B1910+=+0 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-490x%2B1910+=+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=%28-490%29%5E2-4%2A9%2A1910=171340 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-490%29%5E2-4%2A9%2A1910=171340\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=171340 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--490%2B-sqrt%28+171340+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--490%2B-sqrt%28+171340+%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-%28-490%29%2Bsqrt%28+171340+%29%29%2F2%5C9+=+50.218464534692 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-490%29%2Bsqrt%28+171340+%29%29%2F2%5C9+=+50.218464534692\"   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-%28-490%29-sqrt%28+171340+%29%29%2F2%5C9+=+4.22597990975241 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-490%29-sqrt%28+171340+%29%29%2F2%5C9+=+4.22597990975241\"   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=9x%5E2%2B-490x%2B1910 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-490x%2B1910\"   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=9x%5E2%2B-490x%2B1910+=+%28x-50.218464534692%29%2A%28x-4.22597990975241%29 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-490x%2B1910+=+%28x-50.218464534692%29%2A%28x-4.22597990975241%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 50.218464534692, 4.22597990975241.\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+9%2Ax%5E2%2B-490%2Ax%2B1910+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-490%2Ax%2B1910+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "r = 50.22 going, 40.22 returning<BR>\n" );
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document.write( "Ignore the 4... solution, subtracting 10 would give a negative speed. </SPAN>\n" );
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