document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005093>Question 1005093</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me set up this question: A plane that can fly 200 mph in still air makes a 330 mile flight with a tail wind and returns flying into the same wind. Find the speed of the wind if the total flying time is 3 1/3 hours. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621396 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> speed of the plane = 200 miles per hour.\r<BR>\n" );
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document.write( "let w = the speed of the wind.\r<BR>\n" );
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document.write( "with the wind, the combined speed of the plane and the wind is 200 + w.\r<BR>\n" );
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document.write( "against the wind, the combined speed of the plane and the wind is 200 - w.\r<BR>\n" );
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document.write( "the plane travels 330 miles with the wind and 330 miles against the wind.\r<BR>\n" );
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document.write( "total flying time is 3 and 1/3 hours = 10/3 hours.\r<BR>\n" );
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document.write( "let T1 = the amount of time it takes flying with the wind.\r<BR>\n" );
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document.write( "let T2 = the amount of time it takes flying against the wind.\r<BR>\n" );
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document.write( "the rate * time = distance equations become:\r<BR>\n" );
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document.write( "(200 + w) * T1 = 330\r<BR>\n" );
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document.write( "(200 - w) * T2 = 330\r<BR>\n" );
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document.write( "solve for T1 and T2 to get:\r<BR>\n" );
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document.write( "T1 = 330 / (200 + w)\r<BR>\n" );
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document.write( "T2 = 330 / (200 - w)\r<BR>\n" );
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document.write( "since T1 + T2 is equal to 3 and 1/3 hours = 10/3 hours, we get:\r<BR>\n" );
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document.write( "T1 + T2 = 10/3 hours.\r<BR>\n" );
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document.write( "after your replace T1 and T2 with their equivalents, the equation becomes:\r<BR>\n" );
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document.write( "330 / (200 + w) + 330 / (200 - w) = 10/3\r<BR>\n" );
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document.write( "multiply both sides of this equation by 3 and divide both sides of this equation by 10 to get:\r<BR>\n" );
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document.write( "99 / (200 + w) + 99 / (200 - w) = 1\r<BR>\n" );
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document.write( "multiply both sides of this equation by (200 + w) * (200 - w) to get:\r<BR>\n" );
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document.write( "99 * (200 - w) + 99 * (200 + w) = (200 + w) * (200 - w)\r<BR>\n" );
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document.write( "the algebra  gets a little ugly, but, when you solve this equation for w, you get:\r<BR>\n" );
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document.write( "w = 20 miles per hour.\r<BR>\n" );
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document.write( "you can confirm this solution is correct by replacing w in the original equations to see what you get:\r<BR>\n" );
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document.write( "the original equations to work with are:\r<BR>\n" );
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document.write( "T1 = 330 / (200 + w)\r<BR>\n" );
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document.write( "T2 = 330 / (200 - w)\r<BR>\n" );
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document.write( "solving for T1 and T2, using w = 20 miles per hour.\r<BR>\n" );
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document.write( "T1 = 1.5 hours\r<BR>\n" );
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document.write( "T2 = 1.833333 hours\r<BR>\n" );
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document.write( "T1 + T2 = 3.33333333..... which is the same as 3 and 1/3 which is the same as 10/3.\r<BR>\n" );
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document.write( "if you need help with the ugly, let me know.\r<BR>\n" );
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document.write( "otherwise i'll assume you can handle it.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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