document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169541>Question 169541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car travels 180mi, a second car, traveling 15mi/h faster than the first car , makes the trip in 1 hr less time. Find the speed of each car. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124999 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=124999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> distance = rate multiplied by time.  let r and t be rate and time of 1st car<BR>\n" );
document.write( "and r+15 and t-1 be rate and time of 2nd car.<BR>\n" );
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document.write( "180=rt----------->t=180/r....eq 1<BR>\n" );
document.write( "180=(r+15)(t-1)...eq 2<BR>\n" );
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document.write( "take t's value from eq 1 and substitute it into eq 2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180=%28r%2B15%29%28%28180%2Fr%29-1%29 ALIGN=MIDDLE  ALT=\"180=%28r%2B15%29%28%28180%2Fr%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180=%28r%2B15%29%28%28180-r%29%2Fr%29 ALIGN=MIDDLE  ALT=\"180=%28r%2B15%29%28%28180-r%29%2Fr%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....multiply by r<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180r=%28r%2B15%29%28180-r%29 ALIGN=MIDDLE  ALT=\"180r=%28r%2B15%29%28180-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....distribute right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180r=180r-r%5E2%2B2700-15r ALIGN=MIDDLE  ALT=\"180r=180r-r%5E2%2B2700-15r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2B15r-2700=0 ALIGN=MIDDLE  ALT=\"r%5E2%2B15r-2700=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=45%29 ALIGN=MIDDLE  ALT=\"highlight%28r=45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=-60%29 ALIGN=MIDDLE  ALT=\"highlight%28r=-60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   throw out negative value<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=45%29 ALIGN=MIDDLE  ALT=\"highlight%28r=45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > rate of 1st car<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r%2B15=60%29 ALIGN=MIDDLE  ALT=\"highlight%28r%2B15=60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > rate of 2nd car:\r<BR>\n" );
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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=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%2B15r%2B-2700+=+0 ALIGN=MIDDLE  ALT=\"1r%5E2%2B15r%2B-2700+=+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=%2815%29%5E2-4%2A1%2A-2700=11025 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2815%29%5E2-4%2A1%2A-2700=11025\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=11025 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+=+%28-15%2B-sqrt%28+11025+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-15%2B-sqrt%28+11025+%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-%2815%29%2Bsqrt%28+11025+%29%29%2F2%5C1+=+45 ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+%28-%2815%29%2Bsqrt%28+11025+%29%29%2F2%5C1+=+45\"   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-%2815%29-sqrt%28+11025+%29%29%2F2%5C1+=+-60 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+%28-%2815%29-sqrt%28+11025+%29%29%2F2%5C1+=+-60\"   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%2B15r%2B-2700 ALIGN=MIDDLE  ALT=\"1r%5E2%2B15r%2B-2700\"   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%2B15r%2B-2700+=+1%28r-45%29%2A%28r--60%29 ALIGN=MIDDLE  ALT=\"1r%5E2%2B15r%2B-2700+=+1%28r-45%29%2A%28r--60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 45, -60.\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%2B15%2Ax%2B-2700+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B15%2Ax%2B-2700+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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