document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130565>Question 130565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A patrol plane flies 220 miles per hour in still air. It carries fuel for 4 hours of safe flying. If it takes off on patrol against a wind of 20 miles per hour, how far can it fly and return safely? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95376 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=95376\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm going to presume that the wind is constant for the entire 4 hour trip.  That means that it will be a head wind for the outbound leg of the trip and a tail wind for the return trip.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If there were no wind, then the true speed and the speed through still air would be the same and the round trip would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A220=880 ALIGN=MIDDLE  ALT=\"4%2A220=880\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles for a patrol range of 440 miles.  One might think that if the outbound speed were reduced by 20 mph because of the wind, but the return leg speed were increased that same 20 mph, that everything would average out and you could still go the same 440 miles out and make it back.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That turns out not to be the case.  If the outbound leg true speed is 200 (220 - 20) and the aircraft flies 440 miles, then the time taken on the outbound trip is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=440%2F200=2.2 ALIGN=MIDDLE  ALT=\"440%2F200=2.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours.  On the return leg, that same 440 miles will take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=440%2F240=1.8333 ALIGN=MIDDLE  ALT=\"440%2F240=1.8333\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours -- and you will run out of gas 2 minutes (0.033... hours) before you get back.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, let's analyze this a little more carefully.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We know that the distance out has to equal the distance back, and we know that the time out plus the time back has to equal 4 hours.  We also know that the distance out is equal to 200 mph times the time out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bo%5D ALIGN=MIDDLE  ALT=\"t%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that the distance back is equal to 240 mph times the time back <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bb%5D ALIGN=MIDDLE  ALT=\"t%5Bb%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Putting this all together we come up with two equations:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240t%5Bb%5D=200t%5Bo%5D ALIGN=MIDDLE  ALT=\"240t%5Bb%5D=200t%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bo%5D%2Bt%5Bb%5D=4 ALIGN=MIDDLE  ALT=\"t%5Bo%5D%2Bt%5Bb%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Rearranging the second equation gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bo%5D=4-t%5Bb%5D ALIGN=MIDDLE  ALT=\"t%5Bo%5D=4-t%5Bb%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can now substitute this expression for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bo%5D ALIGN=MIDDLE  ALT=\"t%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240t%5Bb%5D=200%284-t%5Bb%5D%29 ALIGN=MIDDLE  ALT=\"240t%5Bb%5D=200%284-t%5Bb%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bb%5D ALIGN=MIDDLE  ALT=\"t%5Bb%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240t%5Bb%5D%2B200t%5Bb%5D=800 ALIGN=MIDDLE  ALT=\"240t%5Bb%5D%2B200t%5Bb%5D=800\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=440t%5Bb%5D=800 ALIGN=MIDDLE  ALT=\"440t%5Bb%5D=800\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bb%5D=20%2F11 ALIGN=MIDDLE  ALT=\"t%5Bb%5D=20%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or the repeating decimal 1.81...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bo%5D ALIGN=MIDDLE  ALT=\"t%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-20%2F11=24%2F11 ALIGN=MIDDLE  ALT=\"4-20%2F11=24%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or the repeating decimal 2.09...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, if the aircraft travels at 200 mph for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F11 ALIGN=MIDDLE  ALT=\"24%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours, then the distance travelled is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2824%2F11%29=4800%2F11 ALIGN=MIDDLE  ALT=\"200%2824%2F11%29=4800%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or the repeating decimal 436.36...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As a check, the return distance must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%2820%2F11%29=4800%2F11 ALIGN=MIDDLE  ALT=\"240%2820%2F11%29=4800%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, answer checks. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );