document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909916>Question 909916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lisa traveled 1040 mi at a certain speed. If the speed had been 13 mph faster, the trip could have been in 4 hr. less time. Find the speed.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #552117 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=552117\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Set Up<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1040%2Fr+-+1040%2F%28r%2B13%29+=+4 ALIGN=MIDDLE  ALT=\"1040%2Fr+-+1040%2F%28r%2B13%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >   |Multiplying thru by r(r+13) so as all denominators = 1<BR>\n" );
document.write( "1040(r+13) - 1040r = 4r^2 + 52r<BR>\n" );
document.write( "4r^2 +52r - 13(1040) = 0<BR>\n" );
document.write( "r^2 + 13r - 13(260) = 0<BR>\n" );
document.write( "r^2 + 13r - 3380 = 0 (Tossing out the negative solution for unit measure)<BR>\n" );
document.write( "r = 52mph.  65mph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52%2B13 ALIGN=MIDDLE  ALT=\"52%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" > to save 4hrs<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=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=1x%5E2%2B13x%2B-3380+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B13x%2B-3380+=+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=%2813%29%5E2-4%2A1%2A-3380=13689 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2813%29%5E2-4%2A1%2A-3380=13689\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=13689 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+=+%28-13%2B-sqrt%28+13689+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-13%2B-sqrt%28+13689+%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-%2813%29%2Bsqrt%28+13689+%29%29%2F2%5C1+=+52 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+13689+%29%29%2F2%5C1+=+52\"   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-%2813%29-sqrt%28+13689+%29%29%2F2%5C1+=+-65 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2813%29-sqrt%28+13689+%29%29%2F2%5C1+=+-65\"   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=1x%5E2%2B13x%2B-3380 ALIGN=MIDDLE  ALT=\"1x%5E2%2B13x%2B-3380\"   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=1x%5E2%2B13x%2B-3380+=+1%28x-52%29%2A%28x--65%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B13x%2B-3380+=+1%28x-52%29%2A%28x--65%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 52, -65.\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%2B13%2Ax%2B-3380+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B13%2Ax%2B-3380+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );