document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033225>Question 1033225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airplane flying against the wind travels 125 miles in the same amount of time it would take the same plane to travel 155 miles with the wind. If the wind speed is a constant 30 miles per hour, how fast would the plane travel in still air? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647859 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=647859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.\r<BR>\n" );
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document.write( "rate is composed of the speed of the plane plus or minus the speed of the wind.\r<BR>\n" );
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document.write( "if we let p = the speed of the plane and w = the speed of the wind and t = the time and d = the distance, you get:\r<BR>\n" );
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document.write( "when the plane is flying against the wind, you get (p-w)*t = d.<BR>\n" );
document.write( "when the plane is flying with the wind, you get (p+w)*t = d.\r<BR>\n" );
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document.write( "when the plane is flying against the wind, you are given that d = 125.<BR>\n" );
document.write( "when the plane is flying with the wind, you are given that d = 155.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "(p-w)*t = 125<BR>\n" );
document.write( "(p+w)*t = 255\r<BR>\n" );
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document.write( "you are given that w = 30, so these formulas become:\r<BR>\n" );
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document.write( "(p-30)*t = 125<BR>\n" );
document.write( "(p+30)*t = 155\r<BR>\n" );
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document.write( "these are two equations that need to be solved simultaneously because the same value of p and the same value of t applies to both of them.\r<BR>\n" );
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document.write( "solve for t in both equation to get:\r<BR>\n" );
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document.write( "t = 125/(p-30)<BR>\n" );
document.write( "t = 155/(p+30)\r<BR>\n" );
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document.write( "since both expressions on the right side of these equations are equal to t, you can set those expressions equal to each other to get:\r<BR>\n" );
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document.write( "125/(p-30) = 155/(p+30)\r<BR>\n" );
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document.write( "multiply both sides of this equation by (p-30)*(p+30) to get:\r<BR>\n" );
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document.write( "125 * (p+30) = 155 * (p-30)\r<BR>\n" );
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document.write( "simplify to get 125 * p + 125*30 = 155 * p - 155 * 30\r<BR>\n" );
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document.write( "simplify to get 125 * p + 3750 = 155 * p - 4650\r<BR>\n" );
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document.write( "subtract 125 * p from both sides of the equation and add 4650 to both sides of the equation to get 3750 + 4650 = 155 * p - 125 * p\r<BR>\n" );
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document.write( "simplify to get 8400 = 30 * p\r<BR>\n" );
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document.write( "divide both sides of this equation by 30 to get 280 = p\r<BR>\n" );
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document.write( "that's the speed of the plane in still air (without any wind).\r<BR>\n" );
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document.write( "this one is a little more difficult than the usual rate * time problem because you can get into trouble when eliminating variables.\r<BR>\n" );
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document.write( "the way above was one way.\r<BR>\n" );
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document.write( "another way would be:\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "(p-30)*t = 125<BR>\n" );
document.write( "(p+30)*t = 155\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "pt - 30t = 125<BR>\n" );
document.write( "pt + 30t = 155\r<BR>\n" );
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document.write( "add the second equation to the first equation to get:\r<BR>\n" );
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document.write( "2pt = 280\r<BR>\n" );
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document.write( "divide both equations by 2 to get pt = 140.\r<BR>\n" );
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document.write( "solve for t to get t = 140/p.\r<BR>\n" );
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document.write( "you still don't have a solution, but you do have a relationship that you can use.\r<BR>\n" );
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document.write( "go back to one of your equations that you started with.\r<BR>\n" );
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document.write( "the one i chose is (p-30)*t = 125\r<BR>\n" );
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document.write( "replace t with 140/p to get:\r<BR>\n" );
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document.write( "(p-30)*140/p = 125\r<BR>\n" );
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document.write( "multiply both sides of this equation by p to get (p-30)*140 = 125*p\r<BR>\n" );
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document.write( "simplify to get 140*p - 30*140 = 125*p\r<BR>\n" );
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document.write( "simplify to get 140*p - 4200 = 125*p\r<BR>\n" );
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document.write( "subtract 125*p from both sides of the equation and add 4200 to both sides of the equation to get:\r<BR>\n" );
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document.write( "140*p - 125*p = 4200\r<BR>\n" );
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document.write( "simplify to get 15*p - 4200\r<BR>\n" );
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document.write( "solve for p to get p = 4200 / 15 = 280.\r<BR>\n" );
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document.write( "you get the plane's speed in still air is 280.\r<BR>\n" );
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document.write( "that's the same as we got above using a different method.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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