document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286237>Question 286237</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airplane makes a 990 km flight with a tailwind and returns, flying into the same wind. The total flying time is 3 hours and 20 minutes, and the airplane's speed in still air is 600 km/h. What is 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 #207738 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=207738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An airplane makes a 990 km flight with a tailwind and returns, flying into the same wind. The total flying time is 3 hours and 20 minutes, and the airplane's speed in still air is 600 km/h. What is the speed of the wind?\r<BR>\n" );
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document.write( "D distance = R rate * T time\r<BR>\n" );
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document.write( "air speed still air + tail wind speed = speed with tail wind<BR>\n" );
document.write( "(or Vg1 = Va + Vw or 600 + Vw = Vg1)<BR>\n" );
document.write( "air speed still air - tail wind speed = speed without tail wind<BR>\n" );
document.write( "(or Vg2 = Va - Vw or 600 - Vw = Vg2)<BR>\n" );
document.write( "T = T1 + T2 = 10/3 hrs<BR>\n" );
document.write( "T2 = 10/3 - T1<BR>\n" );
document.write( "990 = Vg1T1 = Vg2T2<BR>\n" );
document.write( "Vw = Vg1 - 600<BR>\n" );
document.write( "-Vw = Vg2 - 600 --> Vw = 600 - Vg2<BR>\n" );
document.write( "Vg1 - 600 = 600 - Vg2<BR>\n" );
document.write( "Vg1 + Vg2 = 1200<BR>\n" );
document.write( "Vg2 = 1200 - Vg1<BR>\n" );
document.write( "Vg1 * T1 = (1200 - Vg1)* (10/3 - T1)<BR>\n" );
document.write( "Vg1T1 = 4000 - 1200T1 - (10/3)Vg1 + Vg1T1<BR>\n" );
document.write( "0 = 4000 - 1200T1 - (10/3)Vg1<BR>\n" );
document.write( "0 = 4000 - 1200(990/Vg1) - (10/3)Vg1<BR>\n" );
document.write( "0 = 4000Vg1 - 1188000 - (10/3)Vg1^2<BR>\n" );
document.write( "0 = 1200Vg1 - 356400 - Vg1^2<BR>\n" );
document.write( "Vg1^2 - 1200Vg1 + 356400 = 0 (rearranged)<BR>\n" );
document.write( "(Vg1 - 540)(Vg1 - 660) = 0<BR>\n" );
document.write( "check with FOIL: Vg1^2 - 660Vg1 - 540Vg1 + 356400<BR>\n" );
document.write( "Vg1 = 540 or 660<BR>\n" );
document.write( "Vg1 > Vg2 therefore Vg1 is 660<BR>\n" );
document.write( "Vg1 = 660 = Va + Vw = 600 + Vw --> Vw = 60<BR>\n" );
document.write( "then: Vg2 = 540 = Va - Vw = 600 - Vw --> Vw = 60<BR>\n" );
document.write( "check: 990 = 660 * T1, 990 = 540 * T2<BR>\n" );
document.write( "1.5 hours = T1<BR>\n" );
document.write( "990/540 = 99/54 = 33/18 = 11/6 hours = T2<BR>\n" );
document.write( "T1 + T2 = 1.5 hours + 11/6 hours = 3/2 + 11/6 = 9/6 + 11/6 = 20/6 = 10/3 hours<BR>\n" );
document.write( "T1 + T2 = 3 hours and 20 minutes\r<BR>\n" );
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document.write( "Wind Speed is 60 km/hr\r<BR>\n" );
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document.write( " </SPAN>\n" );
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