document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=834486>Question 834486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A jet plane, flying 90 mph faster than a propeller plane, travels 5670 miles in 4 hours less time than the propeller plane takes to fly the same distance. How fast does each plane fly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503027 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=503027\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two Unknowns:<BR>\n" );
document.write( "r = speed of propeller plane<BR>\n" );
document.write( "t = time for propeller plane<BR>\n" );
document.write( "constants:<BR>\n" );
document.write( "k = 90 mph, a speed difference<BR>\n" );
document.write( "h = 4 hour, how much less time needed of the jet<BR>\n" );
document.write( "d = 5670 mile trip\r<BR>\n" );
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document.write( "PLANE___________speed_________time______________distance<BR>\n" );
document.write( "JET_____________r+k___________t-h_______________d<BR>\n" );
document.write( "PROPELLER_______r_____________t_________________d\r<BR>\n" );
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document.write( "I have already solved a few of this general form travel problem recently, so this will be a very abbreviated solution.\r<BR>\n" );
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document.write( "EQUATIONS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28%28r%2Bk%29%28t-h%29=d%29 ALIGN=MIDDLE  ALT=\"highlight_green%28%28r%2Bk%29%28t-h%29=d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28rt=d%29 ALIGN=MIDDLE  ALT=\"highlight_green%28rt=d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve this system for r and t.  You will get a quadratic equation in either t or r.  The way I have solved these, I substituted for t from the simpler equation and first solved for a formula for r.  The quadratic equation I had used was in r. </SPAN>\n" );
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