document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1008675>Question 1008675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr. Martin traveled to a city 150 miles from his home to attend a meeting.  Due to car trouble, his average speed returning was 10 mph less than his speed going.  If the total time for the round trip was 5 hours, at what rate of speed did he travel to the city? (Round your answer to the nearest tenth.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629306 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=629306\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "R=rate going to other city<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150mi%2FR%2B150mi%2F%28R-10%29=5 ALIGN=MIDDLE  ALT=\"150mi%2FR%2B150mi%2F%28R-10%29=5\"   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=%28%28150mi%29%28R-10%29%29%2F%28%28R%29%28R-10%29%29%2B%28%28150mi%29%28R%29%29%2F%28%28R%29%28R-10%29%29=5 ALIGN=MIDDLE   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=%28%28150mi%29%28R-10%29%2B%28150mi%29%28R%29%29%2F%28R%29%28R-10%29=5 ALIGN=MIDDLE  ALT=\"%28%28150mi%29%28R-10%29%2B%28150mi%29%28R%29%29%2F%28R%29%28R-10%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150R-1500%2B150R=5%28R%29%28R-10%29 ALIGN=MIDDLE  ALT=\"150R-1500%2B150R=5%28R%29%28R-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300R-1500=5R%5E2-50R ALIGN=MIDDLE  ALT=\"300R-1500=5R%5E2-50R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=5R%5E2-350R%2B1500 ALIGN=MIDDLE  ALT=\"0=5R%5E2-350R%2B1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=R%5E2-70R%2B300 ALIGN=MIDDLE  ALT=\"0=R%5E2-70R%2B300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=aR%5E2%2BbR%2Bc=0 ALIGN=MIDDLE  ALT=\"aR%5E2%2BbR%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1R%5E2%2B-70R%2B300+=+0 ALIGN=MIDDLE  ALT=\"1R%5E2%2B-70R%2B300+=+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=R%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"R%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=%28-70%29%5E2-4%2A1%2A300=3700 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-70%29%5E2-4%2A1%2A300=3700\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3700 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--70%2B-sqrt%28+3700+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--70%2B-sqrt%28+3700+%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=R%5B1%5D+=+%28-%28-70%29%2Bsqrt%28+3700+%29%29%2F2%5C1+=+65.4138126514911 ALIGN=MIDDLE  ALT=\"R%5B1%5D+=+%28-%28-70%29%2Bsqrt%28+3700+%29%29%2F2%5C1+=+65.4138126514911\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D+=+%28-%28-70%29-sqrt%28+3700+%29%29%2F2%5C1+=+4.5861873485089 ALIGN=MIDDLE  ALT=\"R%5B2%5D+=+%28-%28-70%29-sqrt%28+3700+%29%29%2F2%5C1+=+4.5861873485089\"   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=1R%5E2%2B-70R%2B300 ALIGN=MIDDLE  ALT=\"1R%5E2%2B-70R%2B300\"   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=1R%5E2%2B-70R%2B300+=+1%28R-65.4138126514911%29%2A%28R-4.5861873485089%29 ALIGN=MIDDLE  ALT=\"1R%5E2%2B-70R%2B300+=+1%28R-65.4138126514911%29%2A%28R-4.5861873485089%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 65.4138126514911, 4.5861873485089.\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-70%2Ax%2B300+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-70%2Ax%2B300+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( ".<BR>\n" );
document.write( "Since 4.5 does not work (returning was 10 mph less would<BR>\n" );
document.write( "result in negative speed), his rate going to the city was<BR>\n" );
document.write( "65.4 mph.<BR>\n" );
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document.write( "ANSWER: His rate traveling to the city was 65.4 mph<BR>\n" );
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document.write( "CHECK:<BR>\n" );
document.write( "150 mi/65.4mph+150mi/55.4mph = 5 hours<BR>\n" );
document.write( "2.29 hours + 2.71 hours = 5 hours<BR>\n" );
document.write( "5 hours = 5 hours <BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );