document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137928>Question 1137928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane travels at a speed of 175mph in still air. Flying with a tailwind, the plane is clocked over a distance of 1000 miles. Flying against a headwind, it takes 1 hour longer to complete the return trip. What was the wind velocity? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755804 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=755804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r * t = d<BR>\n" );
document.write( "r = rate<BR>\n" );
document.write( "t = time<BR>\n" );
document.write( "d = distance\r<BR>\n" );
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document.write( "plane flies at 175 mph.\r<BR>\n" );
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document.write( "distance = 1000 miles.\r<BR>\n" );
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document.write( "plane flies with the wind in one direction and against the wind in the other direction.\r<BR>\n" );
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document.write( "it takes t hours with the wind and t + 1 hour against the wind.\r<BR>\n" );
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document.write( "w = the speed of the wind.\r<BR>\n" );
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document.write( "with the wind, the formula becomes (175 + w) * t = 1000\r<BR>\n" );
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document.write( "against the wind, the formula becomes (175 - w) * (t + 1) = 1000\r<BR>\n" );
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document.write( "since they're both equal to 1000, you get:\r<BR>\n" );
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document.write( "(175 + w) * t = (175 - w) * (t + 1)\r<BR>\n" );
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document.write( "simplify each side of this equation t0 get:\r<BR>\n" );
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document.write( "175 * t + w * t = 175 * t + 175 - w * t - w\r<BR>\n" );
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document.write( "subtract 175 * t from both sides of the equation to get:\r<BR>\n" );
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document.write( "w * t = 175 - w * t - w\r<BR>\n" );
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document.write( "add w * t to both sides of the equation to get:\r<BR>\n" );
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document.write( "2 * w * t = 175 - w\r<BR>\n" );
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document.write( "add w to both sides of the equation to get:\r<BR>\n" );
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document.write( "2 * w * t + w = 175\r<BR>\n" );
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document.write( "factor out the w to get:\r<BR>\n" );
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document.write( "w * (2t + 1) = 175\r<BR>\n" );
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document.write( "solve for w to get:\r<BR>\n" );
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document.write( "w = 175 / (2t + 1)\r<BR>\n" );
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document.write( "simplify the first equation of (175 + w) * t = 1000 to get:\r<BR>\n" );
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document.write( "175 * t + w * t = 1000\r<BR>\n" );
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document.write( "replace w with 175 / (2t + 1) to get:\r<BR>\n" );
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document.write( "175 * t + 175 / (2t + 1) * t = 1000\r<BR>\n" );
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document.write( "multiply both sides of this equation by (2t + 1) to get:\r<BR>\n" );
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document.write( "175 * t * (2t + 1) + 175 * t = 1000 * (2t + 1)\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "350 * t^2 + 175 * t + 175 * t = 2000 * t + 1000\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "350 * t^2 + 350 * t = 2000 * t + 1000\r<BR>\n" );
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document.write( "subtract 2000 * t and subtract 1000 from both sides of the equation to get:\r<BR>\n" );
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document.write( "350 * t^2 - 1650 * t - 1000 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get:\r<BR>\n" );
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document.write( "t = 5.257705786321 or t = -0.54342007203528\r<BR>\n" );
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document.write( "t can't be negative, so t = 5.257705786321\r<BR>\n" );
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document.write( "replace t in the first equation with 5.257705786321 to get:\r<BR>\n" );
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document.write( "(175 + w) * t = 1000 becomes (175 + w) * 5.257705786321 = 1000\r<BR>\n" );
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document.write( "simplify this equation to get 920.098512606 + 5.257705786321 * w = 1000\r<BR>\n" );
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document.write( "solve for w to get:\r<BR>\n" );
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document.write( "w = (1000 - 920.098512606) / 5.257705786321 = 15.197025212\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "t = 5.257705786321<BR>\n" );
document.write( "w = 15.197025212\r<BR>\n" );
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document.write( "(175 + w) * t = 1000 becomes (175 + 15.197025212) * 5.257705786321 = 1000 which becomes 1000 = 1000 which is true.\r<BR>\n" );
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document.write( "(175 - w) * (t + 1) = 1000 becomes (175 - 15.197025212) * (5.257705786321 + 1) = 1000 which becomes 1000 = 1000 which is true.\r<BR>\n" );
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document.write( "solution is confirmed to be good.\r<BR>\n" );
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document.write( "your solution is that the velocity of the wind is 15.197025212 miles per hour in the original direction of the trip.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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