document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=991509>Question 991509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At 12-noon flight 237 leaves Chicago headed due south and traveling at a rate of r miles per hour.  At  12-noon a second flight, flight 875, left Chicago from a different runway headed due east and traveling 40 miles per hour slower than flight 237.  At 3:00pm the planes are 600 miles apart. How fast is flight 237 traveling? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611506 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=611506\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At 12-noon flight 237 leaves Chicago headed due south and traveling at a rate of r miles per hour.<BR>\n" );
document.write( " At 12-noon a second flight, flight 875, left Chicago from a different runway headed due east and traveling 40 miles per hour slower than flight 237.<BR>\n" );
document.write( "Therefore<BR>\n" );
document.write( "(r-40) = rate of the flt 875<BR>\n" );
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document.write( " At 3:00pm the planes are 600 miles apart.<BR>\n" );
document.write( "travel time of both planes is 3 hr<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "3r = dist traveled by flt 237<BR>\n" );
document.write( "3(r-40) = (3r-120) = dist traveled by flt 875<BR>\n" );
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document.write( " How fast is flight 237 traveling?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "They are flying at right angles to one another, this is a pythag problem<BR>\n" );
document.write( "a^2 + b^2 = c^2, where<BR>\n" );
document.write( "a = 3r<BR>\n" );
document.write( "b = 3(r-40)<BR>\n" );
document.write( "c = 600<BR>\n" );
document.write( "(3r)^2 + (3r-120)^2 = 600^2<BR>\n" );
document.write( "9r^2 + (9r^2 - 720r + 14400) = 360000<BR>\n" );
document.write( "18r^2 - 720r + 14400 - 360000 = 0<BR>\n" );
document.write( "18r^2 - 720r - 345600 = 0<BR>\n" );
document.write( "simplify, divide by 18<BR>\n" );
document.write( "r^2 - 40r - 19200 = 0<BR>\n" );
document.write( "you can use the quadratic formula. a=1; b=-40; c=-19200, but it will factor to<BR>\n" );
document.write( "(r+120)(r-160) = 0<BR>\n" );
document.write( "The positive solution<BR>\n" );
document.write( "r = 160 mph, flt 237<BR>\n" );
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document.write( ";<BR>\n" );
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document.write( "Check this find the dist each traveled<BR>\n" );
document.write( "flt 237: 3*160 = 480 mi<BR>\n" );
document.write( "flt 875: 3*120 = 360 mi<BR>\n" );
document.write( "Enter in your calc<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28480%5E2+%2B+360%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28480%5E2+%2B+360%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > resulting in 600<BR>\n" );
document.write( " </SPAN>\n" );
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