document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171013>Question 1171013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a plane traveled \"2835\" miles with the wind in 4.5 hours and \"2475\" miles against the wind in the same amount of time. find 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 #795893 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=795893\">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( "with the wind, the rate is additive.<BR>\n" );
document.write( "let p equal the rate of the plane and w equal the rate of the wind.<BR>\n" );
document.write( "the combined rate is (p + w).\r<BR>\n" );
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document.write( "against the wind, the rate is subtractive.<BR>\n" );
document.write( "let p equal the rate of the plane and w equal the rate of the wind.<BR>\n" );
document.write( "the combined rate is (p - w).\r<BR>\n" );
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document.write( "with the wind, the plane traveled 2835. miles in 4.5 hours.<BR>\n" );
document.write( "the formula for that is:<BR>\n" );
document.write( "(p + w) * 4.5 = 2835.\r<BR>\n" );
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document.write( "against the wind, the place traveled 2475 miles in the same amount of time.<BR>\n" );
document.write( "the formula for that is:<BR>\n" );
document.write( "(p - w) * 4.5 = 2475.\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "(p + w) * 4.5 = 2835.<BR>\n" );
document.write( "(p - w) * 4.5 = 2475.\r<BR>\n" );
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document.write( "simplify these equations to get:<BR>\n" );
document.write( "4.5 * p + 4.5 * w = 2835.<BR>\n" );
document.write( "4.5 * p - 4.5 * w = 2475\r<BR>\n" );
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document.write( "add these two equations together to get:|<BR>\n" );
document.write( "9 * p = 5310<BR>\n" );
document.write( "solve for p to get:<BR>\n" );
document.write( "p = 5310 / 9 = 590<BR>\n" );
document.write( "that's the speed of the plane.\r<BR>\n" );
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document.write( "go back to the two equations that need to be solved simultaneously and replace p with 590 to get:<BR>\n" );
document.write( "(p + w) * 4.5 = 2835 becomes (590 + w) * 4.5 = 2835<BR>\n" );
document.write( "(p - w) * 4.5 = 2475 becomes (590 - w) * 4.5 = 2475\r<BR>\n" );
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document.write( "simplify to get:<BR>\n" );
document.write( "4.5 * 590 + 4.5 * w = 2835<BR>\n" );
document.write( "4.5 * 590 - 4.5 * w = 2475.\r<BR>\n" );
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document.write( "in the first of these equations, simplify and solve for w to get:<BR>\n" );
document.write( "w = (2835 - 2655) / 4.5 = 40\r<BR>\n" );
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document.write( "in the second of these equations, simplify and solve for w to get:<BR>\n" );
document.write( "w = (2475 - 2655) / -4.5 = 40\r<BR>\n" );
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document.write( "looks like the speed of the wind is 40 miles per hour and the speed of the plane is 590 miles per hour.\r<BR>\n" );
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document.write( "replace p and w with those values in the original equations to get:\r<BR>\n" );
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document.write( "(p + w) * 4.5 = 2835 becomes (590 + 40) * 4.5 = 2835 which becomes 630 * 4.5 = 2835 which becomes 2835 = 2835 which is true.\r<BR>\n" );
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document.write( "(p - w) * 4.5 = 2475 becomes (590 - 40) * 4.5 = 2475 which becomes 550 * 4.5 = 2475 which becomes 2475 = 2475 which is true.\r<BR>\n" );
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document.write( "your solution is that the speed of the wind is 40 miles per hour.<BR>\n" );
document.write( "this solution has been confirmed to be good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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