document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001626>Question 1001626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem. I was never good with word problems. Please show all steps.\r<BR>\n" );
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document.write( "A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes. What is his speed in still air, and how fast is the wind blowing?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618786 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=618786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = speed of the plane<BR>\n" );
document.write( "let y = speed of the wind.\r<BR>\n" );
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document.write( "rate * time = distance.\r<BR>\n" );
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document.write( "when going against the wind, you subtract the wind speed from the plane speed.<BR>\n" );
document.write( "when going with the wind, you add the wind speed to the plane speed.\r<BR>\n" );
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document.write( "distance = 180.\r<BR>\n" );
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document.write( "going against the wind, the formula becomes (x-y)*2 = 180\r<BR>\n" );
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document.write( "2 is the time and 180 is the distance.\r<BR>\n" );
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document.write( "coming back with the wind, the formula becomes (x+y)*1.2 = 180\r<BR>\n" );
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document.write( "1.2 is the time and 180 is the distance.\r<BR>\n" );
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document.write( "1.2 hours is the same as 1 hours and 12 minutes, because 12 minutes / 60 minutes in an hour = .2 hours.\r<BR>\n" );
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document.write( "you have 2 formulas that need to solved simultaneously, meaning that the same solution has to satisfy both equations.\r<BR>\n" );
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document.write( "the 2 equations are:\r<BR>\n" );
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document.write( "(x-y)*2 = 180<BR>\n" );
document.write( "(x+y)*1.2 = 180\r<BR>\n" );
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document.write( "you solve these like you solve any 2 equations that have to be solved simultaneously.\r<BR>\n" );
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document.write( "one method i use is to just subtrct the second equation from the first after removing parentheses.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "2x - 2y = 180<BR>\n" );
document.write( "subtract 1.2x + 1.2y = 180 from that to get:<BR>\n" );
document.write( "2x - 1.2x = .8x<BR>\n" );
document.write( "-2y - 1.2y = -3.2y<BR>\n" );
document.write( "180 - 180 = 0<BR>\n" );
document.write( "the result becomes:<BR>\n" );
document.write( ".8x - 3.2y = 0<BR>\n" );
document.write( "add 3.2y to both sides of this euation to get:<BR>\n" );
document.write( ".8x = 3.2y<BR>\n" );
document.write( "divide both sides of this equation by .8 to get:<BR>\n" );
document.write( "x = 3.2y / .8 = 4y\r<BR>\n" );
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document.write( "since x = 4y, you can substitute 4y for x in either equation and then solve for y.\r<BR>\n" );
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document.write( "using the first equation:<BR>\n" );
document.write( "2x - 2y = 180 becomes:<BR>\n" );
document.write( "2*(4y) - 2y = 180 which becomes:<BR>\n" );
document.write( "8y - 2y = 180 which becomes:<BR>\n" );
document.write( "6y = 180\r<BR>\n" );
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document.write( "solve for y to get y = 30.\r<BR>\n" );
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document.write( "now that you know y, you can solve for x.<BR>\n" );
document.write( "you will get x = 120.\r<BR>\n" );
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document.write( "the plane speed is 120 and the winds speed = 30.\r<BR>\n" );
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document.write( "from the first equation:<BR>\n" );
document.write( "2*120 - 2*30 = 180 becomesw 240 - 60 = 180 which is true.\r<BR>\n" );
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document.write( "frm the second equation:<BR>\n" );
document.write( "1.2*120 + 1.2*30 = 180 becomes 144 + 36 = 180 which is also true.\r<BR>\n" );
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document.write( "the solution is confirmed as good.\r<BR>\n" );
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document.write( "plane speed is 120 miles per hour.<BR>\n" );
document.write( "wind speed is 30 miles per hour.\r<BR>\n" );
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