document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=646262>Question 646262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Marcia flew her ultralight plane to a nearby town against a head wind of 15 km/h in 2 h and 20 minutes. The return trip under the same wind conditions took 1 h and 24 minutes. Find the plane's air speed and the distance to the nearby town. I tried a chart and can't get it in the right order to solve. I have lots of wind problems on my homework assignment and just can't figure it out! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #405810 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=405810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r\"> represent the air speed and let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE d\"> represent the distance to the town.  Also note that 20 minutes is one-third of an hour and 24 minutes is two-fifths of an hour.\r<BR>\n" );
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document.write( "We know that distance equals rate times time, so distance divided by rate must be time.  When flying into the wind, ground speed will be air speed MINUS wind speed, hence the against the wind trip is described by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{r\ -\ 15}\ =\ \frac{7}{3}\">\r<BR>\n" );
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document.write( "And the downwind trip is then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{r\ +\ 15}\ =\ \frac{7}{5}\">\r<BR>\n" );
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document.write( "Cross-multiplying both we get the two-variable system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3d\ =\ 7(r\ -\ 15)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5d\ =\ 7(r\ +\ 15)\">\r<BR>\n" );
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document.write( "This is easily solved by Elimination.  Distribute the 7s across the parentheses.  Multiply the first equation by -1.  Add the two equations to eliminate the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r\"> variable.  Solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE d\">.  Once you have the value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE d\"> substitute back into either equation and then solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r\">.  Et Voilą!\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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