document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=785103>Question 785103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"On a recent trip, a trucker traveled 300 mi at a constant rate. Because of improved road conditions, the trucker then increased the speed by 10 mph. An additional 240 mi was traveled at the increased rate. The entire trip took 16 h. Find the rate of the trucker for the first 300 mi.\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #477366 by </B><A HREF=/tutors/aboutme.mpl?userid=happyhaps><B>happyhaps(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=happyhaps><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=477366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the rate with which trucker traveled the first 300 mi be s mph.<BR>\n" );
document.write( "Now, the Time = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Distance+%2F+speed ALIGN=MIDDLE  ALT=\"Distance+%2F+speed\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "time taken for 300mi + time taken for 240 mi = 16 hours<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2Fs ALIGN=MIDDLE  ALT=\"300%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%2F%28s%2B10%29 ALIGN=MIDDLE  ALT=\"240%2F%28s%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 16<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "16<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2 ALIGN=MIDDLE  ALT=\"s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > -380s -3000 = 0<BR>\n" );
document.write( "Solving this quadratic equation <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=16x%5E2%2B-380x%2B-3000+=+0 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-380x%2B-3000+=+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=%28-380%29%5E2-4%2A16%2A-3000=336400 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-380%29%5E2-4%2A16%2A-3000=336400\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=336400 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--380%2B-sqrt%28+336400+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--380%2B-sqrt%28+336400+%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-%28-380%29%2Bsqrt%28+336400+%29%29%2F2%5C16+=+30 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-380%29%2Bsqrt%28+336400+%29%29%2F2%5C16+=+30\"   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-%28-380%29-sqrt%28+336400+%29%29%2F2%5C16+=+-6.25 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-380%29-sqrt%28+336400+%29%29%2F2%5C16+=+-6.25\"   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=16x%5E2%2B-380x%2B-3000 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-380x%2B-3000\"   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=16x%5E2%2B-380x%2B-3000+=+16%28x-30%29%2A%28x--6.25%29 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-380x%2B-3000+=+16%28x-30%29%2A%28x--6.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 30, -6.25.\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+16%2Ax%5E2%2B-380%2Ax%2B-3000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-380%2Ax%2B-3000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Neglecting the negative solution we get s = 30mph. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );