document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=305798>Question 305798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Amy drove 200 miles to New Orleans at an average speed of 10 miles per hour faster than her usual speed.  If she completed the trip in 1 hour less than usual, what is her usual driving speed, in miles per hour.\r<BR>\n" );
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document.write( "Solve: 200/r+10 = (200/r)-1<BR>\n" );
document.write( "Book says the answer is 40\r<BR>\n" );
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document.write( "How do you simplify the above equation and solve for 40? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218949 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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=218949\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F%28R%2B10%29=+%28200%2FR%29+-1 ALIGN=MIDDLE  ALT=\"200%2F%28R%2B10%29=+%28200%2FR%29+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply everything by (R+10)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200+=+200+%2B+2000%2FR+-+R+-+10 ALIGN=MIDDLE  ALT=\"200+=+200+%2B+2000%2FR+-+R+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200+=+190+%2B+2000%2FR+-+R ALIGN=MIDDLE  ALT=\"200+=+190+%2B+2000%2FR+-+R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply Everything by R<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200R+=+190R+%2B+2000+-+R%5E2 ALIGN=MIDDLE  ALT=\"200R+=+190R+%2B+2000+-+R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 200R from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-10R+%2B+2000+-+R%5E2 ALIGN=MIDDLE  ALT=\"0+=+-10R+%2B+2000+-+R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the 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=-1x%5E2%2B-10x%2B2000+=+0 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-10x%2B2000+=+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=%28-10%29%5E2-4%2A-1%2A2000=8100 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-10%29%5E2-4%2A-1%2A2000=8100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=8100 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--10%2B-sqrt%28+8100+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--10%2B-sqrt%28+8100+%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-%28-10%29%2Bsqrt%28+8100+%29%29%2F2%5C-1+=+-50 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+8100+%29%29%2F2%5C-1+=+-50\"   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-%28-10%29-sqrt%28+8100+%29%29%2F2%5C-1+=+40 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-10%29-sqrt%28+8100+%29%29%2F2%5C-1+=+40\"   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%2B-10x%2B2000 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-10x%2B2000\"   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%2B-10x%2B2000+=+-1%28x--50%29%2A%28x-40%29 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-10x%2B2000+=+-1%28x--50%29%2A%28x-40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -50, 40.\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-10%2Ax%2B2000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-10%2Ax%2B2000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "The quadratic equation gives you two answers: -50, & 40.  Since Amy could not have been driving at a negative rate, 40 is the only answer. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );