document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=523007>Question 523007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A light aircraft flies A to B, 450km away, and back from B and A in a total time of 5 hours and 30 minutes. Suppose that during the whole journey there is a constant wind blowing from A  to B if the speed of the aircraft in still air is 165 km/h find the speed of the wind. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #347158 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=347158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <b>Problem:</b>  A light aircraft flies from A to B, 450km away, and returns from B and A in a total time of 5 hours and 30 minutes. Suppose that during the whole journey there is a constant wind blowing from A  to B.  The speed of the aircraft in still air is 165 km/h. Find the speed of the wind.<BR>\n" );
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document.write( "<b>Solution:</b> The basic approach to solving problems such as these is to begin with the fundamental distance equation and plug in the known values and then solve for the unknowns.<BR>\n" );
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document.write( "d = rt is the basic distance equation.<BR>\n" );
document.write( "d = 450 km<BR>\n" );
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document.write( "We are told the wind is blowing from A to B, so on the trip from A to B the airplane's speed is 165 km/h + w, where 'w' is the wind speed in km/h.  That means the speed across the ground (the ground speed) is faster than the indicated airspeed.  A wind from behind is called a 'tailwind.'<BR>\n" );
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document.write( "Similarly, the ground speed going from B to A will be reduced by the wind. The indicated airspeed will still be 165, but the speed across the ground will be 165 - w.  Such a wind is called a 'headwind.'<BR>\n" );
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document.write( "We must assume the distance from A to B equals the distance from B to A.  That is a reasonable mathematical assumption, although there are many factors in aviation that could force the path to be quite different going and coming. <BR>\n" );
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document.write( "We assume the plane is flying at an indicated airspeed of 165 km/h in both directions.<BR>\n" );
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document.write( "We are told the roundtrip time is 5 hr 30 min, which = 5.5 hr.<BR>\n" );
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document.write( "A to B trip:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450+=+%28165%2Bw%29%2At+ ALIGN=MIDDLE  ALT=\"+450+=+%28165%2Bw%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+450%2F%28165%2Bw%29+ ALIGN=MIDDLE  ALT=\"+t+=+450%2F%28165%2Bw%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "B to A trip:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450+=+%28165-w%29%2A%285.5-t%29+ ALIGN=MIDDLE  ALT=\"+450+=+%28165-w%29%2A%285.5-t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5.5-t+=+450%2F%28165-w%29+ ALIGN=MIDDLE  ALT=\"+5.5-t+=+450%2F%28165-w%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-t+=+450%2F%28165-w%29+-+5.5+ ALIGN=MIDDLE  ALT=\"+-t+=+450%2F%28165-w%29+-+5.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+-450%2F%28165-w%29+%2B+5.5+ ALIGN=MIDDLE  ALT=\"+t+=+-450%2F%28165-w%29+%2B+5.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+t+ ALIGN=MIDDLE  ALT=\"+t+=+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450%2F%28165%2Bw%29+=+-450%2F%28165-w%29+%2B+5.5+ ALIGN=MIDDLE  ALT=\"+450%2F%28165%2Bw%29+=+-450%2F%28165-w%29+%2B+5.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450%2F%28165%2Bw%29+%2B+450%2F%28165-w%29+=+5.5+ ALIGN=MIDDLE  ALT=\"+450%2F%28165%2Bw%29+%2B+450%2F%28165-w%29+=+5.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+450%2A%28165-w%29+%2B+450%2A%28165%2Bw%29+%29+%2F+%28+%28165%2Bw%29%2A%28165-w%29+%29+=+5.5+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+450%2A%28165-w%29+%2B+450%2A%28165%2Bw%29+%29+=+%28+%28165%2Bw%29%2A%28165-w%29+%29+%2A+5.5+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450%2A%28165-w%2B165%2Bw%29+=+%28165%5E2+-165w+%2B+165w+-w%5E2%29+%2A+5.5+ ALIGN=MIDDLE  ALT=\"+450%2A%28165-w%2B165%2Bw%29+=+%28165%5E2+-165w+%2B+165w+-w%5E2%29+%2A+5.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450%2A330+=+%28165%5E2+-165w+%2B+165w+-w%5E2%29+%2A+5.5+ ALIGN=MIDDLE  ALT=\"+450%2A330+=+%28165%5E2+-165w+%2B+165w+-w%5E2%29+%2A+5.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450%2A330%2F5.5+=+%28165%5E2+-165w+%2B+165w+-w%5E2%29+ ALIGN=MIDDLE  ALT=\"+450%2A330%2F5.5+=+%28165%5E2+-165w+%2B+165w+-w%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+27000+=+-w%5E2+%2B+165%5E2+ ALIGN=MIDDLE  ALT=\"+27000+=+-w%5E2+%2B+165%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%5E2+=+165%5E2+-27000+ ALIGN=MIDDLE  ALT=\"+w%5E2+=+165%5E2+-27000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%5E2+=+27225+-27000+=225+ ALIGN=MIDDLE  ALT=\"+w%5E2+=+27225+-27000+=225+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+15+ ALIGN=MIDDLE  ALT=\"+w+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that sqrt(225) = + or - 15, but a negative wind speed is not applicable.<BR>\n" );
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document.write( "Substitute w = 15<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450+=+%28165%2Bw%29%2At+ ALIGN=MIDDLE  ALT=\"+450+=+%28165%2Bw%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450+=+%28165%2B15%29%2At+ ALIGN=MIDDLE  ALT=\"+450+=+%28165%2B15%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450+=+180t+ ALIGN=MIDDLE  ALT=\"+450+=+180t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180t+=+450+ ALIGN=MIDDLE  ALT=\"+180t+=+450+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+450%2F180+=+45%2F18+=+5%2F2+=+2.5+ ALIGN=MIDDLE  ALT=\"+t+=+450%2F180+=+45%2F18+=+5%2F2+=+2.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is the time flying from A to B with a tailwind.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5.5-t+=+5.5-2.5+=+3+ ALIGN=MIDDLE  ALT=\"+5.5-t+=+5.5-2.5+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is the time flying from B to A with a headwind.<BR>\n" );
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document.write( "Check the distances traveled to be sure this is the answer.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28165%2B15%29%2A2.5+=+450+ ALIGN=MIDDLE  ALT=\"+%28165%2B15%29%2A2.5+=+450+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28165-15%29%2A3+=+450+ ALIGN=MIDDLE  ALT=\"+%28165-15%29%2A3+=+450+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Correct.<BR>\n" );
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document.write( "<b>Answer</b>:  The wind speed is 15 km/h.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );