document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121629>Question 1121629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane can fly 350 mph in still air. If it can fly 205 miles downwind in the same amount of time it can fly 145 miles upwind, find the velocity of the wind.<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 #737591 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=737591\">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( "You cannot find the velocity of the wind with the given information because you have no idea of which direction the wind is blowing.  Velocity is a vector quantity which means that it has both a magnitude (what we generally refer to as \"speed\") and a direction.  \"50 mph\" is a speed.  \"50 mph North\" is a velocity.  Be that as it may, you can express the velocity of the wind relative to the direction of travel of the aircraft, whatever that might be.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r_w\"> represent the speed of the wind.  Relative to the direction of travel then, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -r_w\"> is the velocity of the wind relative to the aircraft when the aircraft is flying against the wind, aka upwind, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large +r_w\"> is the velocity of the wind relative to the aircraft when the aircraft is flying with the wind, aka downwind.\r<BR>\n" );
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document.write( "The speed of the aircraft downwind is then:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 350\ +\ r_w\"> and the speed of the aircraft upwind is then: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 350\ -\ r_w\">.\r<BR>\n" );
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document.write( "Since distance equals rate (aka speed) times time:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (350\ -\ r_w)t\ =\ 145\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (350\ +\ r_w)t\ =\ 205\">\r<BR>\n" );
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document.write( "Which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  t\ =\ \frac{145}{350\ -\ r_w}\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  t\ =\ \frac{205}{350\ +\ r_w}\">\r<BR>\n" );
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document.write( "But since the problem says \"in the same amount of time\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{145}{350\ -\ r_w}\ =\ \frac{205}{350\ +\ r_w}\">\r<BR>\n" );
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document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r_w\">\r<BR>\n" );
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document.write( "Which is the wind speed.  The direction is up to you to discover if you can.<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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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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