document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109935>Question 1109935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> AN AIRPLANE FLYING EAST AT THE RATE OF 6 MILES/MINUTES ,PASSED OVER A COURT-HOUSE AT 2 PM. A SECOND PLANE FLYING NORTH AT THE RATE OF 6 MILES/MINUTES,PASSED OVER THE COURT-HOUSE AT 2:04 PM.IV THE PLANES ARE FLYING AT THE SAME  ALTITUDE ,IN HOW MANY MINUTES AFTER 2 PM WILL THEY BE 36 MILES APART? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724915 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> AN AIRPLANE FLYING EAST AT THE RATE OF 6 MILES/MINUTES ,PASSED OVER A COURT-HOUSE AT 2 PM. A SECOND PLANE FLYING NORTH AT THE RATE OF 6 MILES/MINUTES,PASSED OVER THE COURT-HOUSE AT 2:04 PM. IV THE PLANES ARE FLYING AT THE SAME  ALTITUDE,IN HOW MANY MINUTES AFTER 2 PM WILL THEY BE 36 MILES APART?<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "p = distance of the 1st plane from the courthouse at t minutes past 2<BR>\n" );
document.write( "q = distance of the 2nd plane from the courthouse at t minutes past 2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "t=0 at 2:04<BR>\n" );
document.write( "p = 6t + 4*6 = 6t+24<BR>\n" );
document.write( "q = 6t<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(6t+24)^2 + (6t)^2 = 36^2<BR>\n" );
document.write( "(t+4)^2 + (t)^2 = 36<BR>\n" );
document.write( "2t^2 + 8t -20 = 0<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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=2x%5E2%2B8x%2B-20+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B8x%2B-20+=+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=%288%29%5E2-4%2A2%2A-20=224 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%288%29%5E2-4%2A2%2A-20=224\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=224 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+=+%28-8%2B-sqrt%28+224+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-8%2B-sqrt%28+224+%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-%288%29%2Bsqrt%28+224+%29%29%2F2%5C2+=+1.74165738677394 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%288%29%2Bsqrt%28+224+%29%29%2F2%5C2+=+1.74165738677394\"   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-%288%29-sqrt%28+224+%29%29%2F2%5C2+=+-5.74165738677394 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%288%29-sqrt%28+224+%29%29%2F2%5C2+=+-5.74165738677394\"   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=2x%5E2%2B8x%2B-20 ALIGN=MIDDLE  ALT=\"2x%5E2%2B8x%2B-20\"   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=2x%5E2%2B8x%2B-20+=+%28x-1.74165738677394%29%2A%28x--5.74165738677394%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B8x%2B-20+=+%28x-1.74165738677394%29%2A%28x--5.74165738677394%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.74165738677394, -5.74165738677394.\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+2%2Ax%5E2%2B8%2Ax%2B-20+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B8%2Ax%2B-20+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "========================<BR>\n" );
document.write( "t =~ 1.74 minutes past 2:04<BR>\n" );
document.write( "--> 5.74 minutes past 2:00\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );