document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=487176>Question 487176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two planes leave simultaneously from the same airport, one flying due north and one flying due east. The northbound plane is flying 50 mph faster than the eastbound plane. After 3 hours they are 2440 miles apart. Find the speed of each plane. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332979 by </B><A HREF=/tutors/aboutme.mpl?userid=jorel1380><B>jorel1380(3719)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jorel1380><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=jorel1380><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=332979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (3n-150)2+(3n)2=(2440)2<BR>\n" );
document.write( "9n2-900n+22500+9n2=5953600<BR>\n" );
document.write( "18n2-900n-5931100=0<BR>\n" );
document.write( "9n2-450n-2965550=0<BR>\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=9x%5E2%2B-450x%2B-2965550+=+0 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-450x%2B-2965550+=+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=%28-450%29%5E2-4%2A9%2A-2965550=106962300 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-450%29%5E2-4%2A9%2A-2965550=106962300\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=106962300 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--450%2B-sqrt%28+106962300+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--450%2B-sqrt%28+106962300+%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-%28-450%29%2Bsqrt%28+106962300+%29%29%2F2%5C9+=+599.569887442386 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-450%29%2Bsqrt%28+106962300+%29%29%2F2%5C9+=+599.569887442386\"   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-%28-450%29-sqrt%28+106962300+%29%29%2F2%5C9+=+-549.569887442386 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-450%29-sqrt%28+106962300+%29%29%2F2%5C9+=+-549.569887442386\"   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=9x%5E2%2B-450x%2B-2965550 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-450x%2B-2965550\"   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=9x%5E2%2B-450x%2B-2965550+=+9%28x-599.569887442386%29%2A%28x--549.569887442386%29 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-450x%2B-2965550+=+9%28x-599.569887442386%29%2A%28x--549.569887442386%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 599.569887442386, -549.569887442386.\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+9%2Ax%5E2%2B-450%2Ax%2B-2965550+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-450%2Ax%2B-2965550+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Throwing out the negative answer, we get the speeds of the planes to be approximately 600 mph for the northbound plane, and 550 mph for the eastbound plane.. </SPAN>\n" );
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