document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=831367>Question 831367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A jet plane, flying 160 mph faster than a propeller plane, travels 4800 miles in 5 hours less time than the propeller plane takes to fly the same distance. How fast does each plane fly?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501273 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=501273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This general type of travel problem seems to be becoming common.\r<BR>\n" );
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document.write( "A jet plane, flying v mph faster than a propeller plane, travels d miles in p hours less time than the propeller plane takes to fly the same distance. How fast does each plane fly?   Assume v and p are positive numbers.\r<BR>\n" );
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document.write( "Additionally, let r be the speed of the propeller plane; and let h be the time for the propeller plane to make the d distance.\r<BR>\n" );
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document.write( "_______________speed___________time________________distance<BR>\n" );
document.write( "JET____________r+v____________h-p__________________d<BR>\n" );
document.write( "PROP____________r______________h___________________d\r<BR>\n" );
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document.write( "The UNKNOWN variables are r and h.  Use the uniform rates equation for travel, R*T=D, for Rate, Time, Distance.\r<BR>\n" );
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document.write( "EQUATIONS TO BEGIN:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2Bv%29%28h-p%29=d ALIGN=MIDDLE  ALT=\"%28r%2Bv%29%28h-p%29=d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rh=d ALIGN=MIDDLE  ALT=\"rh=d\"   DISABLED_style= \"max-width:90%; height:auto;\" >;\r<BR>\n" );
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document.write( "The steps will very neatly give a useful equation...<BR>\n" );
document.write( "...starting with the jet's equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rh%2Bvh-rp-vp=d ALIGN=MIDDLE  ALT=\"rh%2Bvh-rp-vp=d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice that we already have the propeller plane's equation rh=d allowing a substitution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Bvh-rp-vp=d ALIGN=MIDDLE  ALT=\"d%2Bvh-rp-vp=d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vh-pr-pv=0 ALIGN=MIDDLE  ALT=\"vh-pr-pv=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can again use the propeller's simple equation, as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=d%2Fr ALIGN=MIDDLE  ALT=\"h=d%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and then get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%28d%2Fr%29-pr-pv=0 ALIGN=MIDDLE  ALT=\"v%28d%2Fr%29-pr-pv=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vd-pr%5E2-pvr=0 ALIGN=MIDDLE  ALT=\"vd-pr%5E2-pvr=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-pr%5E2-pvr%2Bvd=0 ALIGN=MIDDLE  ALT=\"-pr%5E2-pvr%2Bvd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28pr%5E2%2Bpvr-vd=0%29 ALIGN=MIDDLE  ALT=\"highlight%28pr%5E2%2Bpvr-vd=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----QUADRATIC EQUATION IN THE ONE VARIABLE, r.  Use general solution to a quadratic equation to solve for r.  Use found value to get the value for h. </SPAN>\n" );
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