document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=657373>Question 657373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airplane flying north at 320 mph passed over a point on the ground at 2:00 p.m. Another plane at the same altitude passed over the point at 2:15 p.m. <BR>\n" );
document.write( "flying east at 300 mph. At what time will the planes be 500 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 #409865 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=409865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "15 minutes after the northbound plane passes the point on the ground, it will be 0.25 times 320 = 80 miles north of the point on the ground.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\"> represent the number of hours after 2:15 that the two planes are 500 miles apart.  The first plane will travel <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 320t\"> miles north of the 80 mile point north of the original flyover point, so the total distance traveled by the northbound plane starting at the flyover point will be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 320t\ +\ 80\">.  The total distance traveled by the eastbound plane will be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 300t\">.\r<BR>\n" );
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document.write( "These two distances are legs of a right triangle.  We need to find <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\"> such that the hypotenuse of the triangle measures 500 miles.\r<BR>\n" );
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document.write( "Using Pythagoras:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (320t\ +\ 80)^2\ +\ (300t)^2\ =\ 500^2\">\r<BR>\n" );
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document.write( "A little Algebra Music, Sammy...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 102400t^2\ +\ 51200t\ +\ 6400\ +\ 90000t^2\ =\ 250000\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 192400t^2\ +\ 51200t\ -\ 243600\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1924t^2\ +\ 512t\ -\ 2436\ =\ 0\">\r<BR>\n" );
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document.write( "Which factors:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (t\ -\ 1)(1924t\ +\ 2436)\ =\ 0\">\r<BR>\n" );
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document.write( "Toss out the negative root.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\ =\ 1\">\r<BR>\n" );
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document.write( "2:15 PM plus 1 hour is 3:15 PM.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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