document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=358385>Question 358385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airplane flying north at 200 mph passed over a point on the ground at 2:00 PM.  Another airplane at the same altitude passed over the point at 2:30 PM, flying east at 400 mph.  At what time were the planes 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 #255773 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=255773\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An airplane flying north at 200 mph passed over a point on the ground at 2:00 PM.  Another airplane at the same altitude passed over the point at 2:30 PM, flying east at 400 mph.  At what time were the planes 500 miles apart?<BR>\n" );
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document.write( "North plane 200 mph 2.00pm<BR>\n" );
document.write( "East plane 400 mph 2.30 pm<BR>\n" );
document.write( "...<BR>\n" );
document.write( "in 1/2 hour north plan has traveled 100 miles. when other plane passes the point.<BR>\n" );
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document.write( "they are flying at right angles to each other.<BR>\n" );
document.write( "when the east bound plane travels 2x miles north bound plane has traveled x+100 miles. ( because speed is half & it has 1/2 hour lead)<BR>\n" );
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document.write( "(2x)^(x+100)^2= 500^2<BR>\n" );
document.write( "4x^2+x^2+200x+10000=250000<BR>\n" );
document.write( "5x^2+200x-240000=0<BR>\n" );
document.write( "5x^2+1200x-1000x-240000=0<BR>\n" );
document.write( "5x(x+240)-1000(x+240)=0<BR>\n" );
document.write( "(x+240)(5x-1000)=0<BR>\n" );
document.write( "5(x+240)(x-200)=0<BR>\n" );
document.write( "x=200 miles<BR>\n" );
document.write( "2x=400 miles:  speed = 400 mph<BR>\n" );
document.write( "time = distance/speed<BR>\n" );
document.write( "400/400 = 1 hour<BR>\n" );
document.write( "....<BR>\n" );
document.write( "CHECK<BR>\n" );
document.write( "400^2+300^2=500^2 </SPAN>\n" );
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