document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=830872>Question 830872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a jet plane flying 100 mph faster than a propeller plane, travels 3150 miles in 2 hours less time than the propeller plane takes to fly the same distance. what are the speeds of both planes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #500974 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=500974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r for speed of the propeller plane<BR>\n" );
document.write( "h for the time of the propeller plane<BR>\n" );
document.write( "Rate*Time=Distance\r<BR>\n" );
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document.write( "___________________speed_____________time______________distance<BR>\n" );
document.write( "PROP_______________r__________________h__________________3150<BR>\n" );
document.write( "JET_______________r+100_____________h-2__________________3150\r<BR>\n" );
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document.write( "Immediately find two equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rh=3150 ALIGN=MIDDLE  ALT=\"rh=3150\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B100%29%28h-2%29=3150 ALIGN=MIDDLE  ALT=\"%28r%2B100%29%28h-2%29=3150\"   DISABLED_style= \"max-width:90%; height:auto;\" >;\r<BR>\n" );
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document.write( "Working with the jet equation,<BR>\n" );
document.write( "rh+100h-2r-200=3150<BR>\n" );
document.write( "And substituting using the first equation<BR>\n" );
document.write( "3150+100h-2r-200=3150<BR>\n" );
document.write( "r-50h+100=0<BR>\n" );
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document.write( "Now, solving the propellor equation for h, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3150%2Fr ALIGN=MIDDLE  ALT=\"h=3150%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and substitute into jet equation as just found, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-50h%2B100=0 ALIGN=MIDDLE  ALT=\"r-50h%2B100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-50%283150%2Fh%29%2B100=0 ALIGN=MIDDLE  ALT=\"r-50%283150%2Fh%29%2B100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "some steps<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28r%5E2%2B100r-157500=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28r%5E2%2B100r-157500=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Not shown here next, but use of general solution to the quadratic equation will give you ....<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=350%29 ALIGN=MIDDLE  ALT=\"highlight%28r=350%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph<BR>\n" );
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document.write( "SUMMARY:<BR>\n" );
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document.write( "Propeller plane, r=350 mph<BR>\n" );
document.write( "Jet plane, r+100=450 mph<BR>\n" );
document.write( "Travel time propeller, h=9 hour<BR>\n" );
document.write( "Travel time jet, h-2=7 hours<BR>\n" );
document.write( "------------------------------------- </SPAN>\n" );
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