document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=576301>Question 576301</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Two airplanes depart simultaneously from an airport.  One flies due south; the other flies due <BR>\n" );
document.write( "east at a rate 30 mph faster than that of the first airplane.  After 3 hours, radar indicates that <BR>\n" );
document.write( "the airplanes are 450 miles apart.  What is the ground speed of each airplane </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369902 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=369902\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two airplanes depart simultaneously from an airport.<BR>\n" );
document.write( " One flies due south; the other flies due east at a rate 30 mph faster than that of the first airplane.<BR>\n" );
document.write( " After 3 hours, radar indicates that the airplanes are 450 miles apart.<BR>\n" );
document.write( "What is the ground speed of each airplane.<BR>\n" );
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document.write( "let s = speed of the southbound airplane<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+30) = speed of the eastbound<BR>\n" );
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document.write( "dist = time * speed, therefore<BR>\n" );
document.write( "3s = distance traveled by the southbound plane<BR>\n" );
document.write( "and<BR>\n" );
document.write( "3(s+30) = distance traveled by the eastbound plane<BR>\n" );
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document.write( "This is a right triangle problem: a^2 + b^2 = c^2, where<BR>\n" );
document.write( "a = 3s<BR>\n" );
document.write( "b = 3(s+30)<BR>\n" );
document.write( "c = 450<BR>\n" );
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document.write( "(3s)^2 + (3(s+30))^2 = 450^2<BR>\n" );
document.write( "9s^2 + (3s+90)^2 = 202500<BR>\n" );
document.write( "9s^2 + 9s^2 + 270s + 270s + 8100 - 202500 = 0<BR>\n" );
document.write( "18s^2 + 540s - 194400 = 0<BR>\n" );
document.write( "simplify, divide by 18<BR>\n" );
document.write( "s^2 + 30s - 10800 = 0<BR>\n" );
document.write( "you can use the quadratic formula to find s, but this will factor to:<BR>\n" );
document.write( "(s+120)(s-90) = 0<BR>\n" );
document.write( "the positive solution is all we want here<BR>\n" );
document.write( "s = 90 mph, speed of the southbound plane<BR>\n" );
document.write( "then<BR>\n" );
document.write( "90+30 = 120 mph, speed of the eastbound<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this out on your calc: enter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%283%2890%29%29%5E2%2B%283%28120%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%283%2890%29%29%5E2%2B%283%28120%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > results 450<BR>\n" );
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