document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28932>Question 28932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 150 mile trip is driven at R miles per hour. The same trip would take 2 hours less if you increase the speed by 20 mph. What is R?  I have tried R=150/t<BR>\n" );
document.write( "R=150/t-2  (150/t+2=150/t-2).t(t-1)= 150t-150t+2t2-2t= t2-t-150=0 = (t+2)(t+75)and that is as far as I get because I know that that is not right. <BR>\n" );
document.write( "Thank you for your help. These always put me in a tail spin. Cheryl Vogel    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15808 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=15808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> original data: 150=Rt. So, t=150/R<BR>\n" );
document.write( "Modified time and rate result in the following:<BR>\n" );
document.write( "150=(R+20)(t-2)<BR>\n" );
document.write( "Substitue for \"t\" to get:<BR>\n" );
document.write( "150=(R+20)[(150/R)-2]<BR>\n" );
document.write( "150=150-2R+3000/R-40<BR>\n" );
document.write( "0=-2R^2+3000-40R<BR>\n" );
document.write( "0=2R^2+40R-3000<BR>\n" );
document.write( "0=R^2+20R-1500<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%2B20R%2B-1500+=+0 ALIGN=MIDDLE  ALT=\"1R%5E2%2B20R%2B-1500+=+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=%2820%29%5E2-4%2A1%2A-1500=6400 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2820%29%5E2-4%2A1%2A-1500=6400\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=6400 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+=+%28-20%2B-sqrt%28+6400+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-20%2B-sqrt%28+6400+%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-%2820%29%2Bsqrt%28+6400+%29%29%2F2%5C1+=+30 ALIGN=MIDDLE  ALT=\"R%5B1%5D+=+%28-%2820%29%2Bsqrt%28+6400+%29%29%2F2%5C1+=+30\"   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-%2820%29-sqrt%28+6400+%29%29%2F2%5C1+=+-50 ALIGN=MIDDLE  ALT=\"R%5B2%5D+=+%28-%2820%29-sqrt%28+6400+%29%29%2F2%5C1+=+-50\"   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%2B20R%2B-1500 ALIGN=MIDDLE  ALT=\"1R%5E2%2B20R%2B-1500\"   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%2B20R%2B-1500+=+1%28R-30%29%2A%28R--50%29 ALIGN=MIDDLE  ALT=\"1R%5E2%2B20R%2B-1500+=+1%28R-30%29%2A%28R--50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 30, -50.\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%2B20%2Ax%2B-1500+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B20%2Ax%2B-1500+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );