document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117848>Question 117848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i really need help<BR>\n" );
document.write( "  the speed of an airplane in still air in 268mph the plane travels 629mi in a total time of 11hr what is 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 #85850 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For starters, you don't know whether the plane is being helped by the wind (tailwind) or<BR>\n" );
document.write( "is being slowed down by the wind (headwind). <BR>\n" );
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document.write( "Ask yourself, \"If there were no wind, how far would the plane go in the 11 hours that it is<BR>\n" );
document.write( "flying?\" To get that answer you multiply its speed in still air (no wind) by 11 as follows:<BR>\n" );
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document.write( "Distance = 268 miles per hour times 11 hours = 268*11 = 2948 miles<BR>\n" );
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document.write( "But since the plane only flies 629 miles in 11 hours, you know that the wind really has to<BR>\n" );
document.write( "be slowing it down. The plane is flying into a pretty strong headwind because it is really being<BR>\n" );
document.write( "slowed down. <BR>\n" );
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document.write( "If the plane is going directly into a headwind, its true rate of speed is its speed in still<BR>\n" );
document.write( "air minus the speed of the wind that it is flying into. If W is the speed of the headwind, the<BR>\n" );
document.write( "true speed of the plane (268 mph) minus W or (268 - W).<BR>\n" );
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document.write( "Since that is the actual or true speed of the airplane, in 11 hours the distance that the<BR>\n" );
document.write( "plane flies (you are told 629 miles) can be represented by the following equation:<BR>\n" );
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document.write( "Distance = speed * time = (268 - W)*11<BR>\n" );
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document.write( "Multiplying out the right side of this equation results in two products as follows:<BR>\n" );
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document.write( "Distance = 268*11 - 11*W<BR>\n" );
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document.write( "And since the distance is 629 miles, substituting 629 for distance results in the equation<BR>\n" );
document.write( "becoming:<BR>\n" );
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document.write( "629 = 268*11 - 11*W<BR>\n" );
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document.write( "The product of 268 and 11 is 268*11 = 2948. So substitute 2948 into the equation  in place of 268*11<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "629 = 2948 - 11*W<BR>\n" );
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document.write( "Get rid of the 2948 on the right side by subtracting 2948 from both sides to make the equation:<BR>\n" );
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document.write( "629 - 2948 = -11*W<BR>\n" );
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document.write( "and combining the numbers on the left side results in:<BR>\n" );
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document.write( "-2319 = - 11*W<BR>\n" );
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document.write( "Solve this equation for W by dividing both sides by -11, the multiplier of W to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2319%2F-11+=+W ALIGN=MIDDLE  ALT=\"-2319%2F-11+=+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And performing the division on the left side (dividing -2319 by -11) reduces the equation to:<BR>\n" );
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document.write( "210.8181818 = W<BR>\n" );
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document.write( "This tells you that the headwind that the plane flies into is 210.8181818 miles per hour.<BR>\n" );
document.write( "(Round this off to 210.8 miles per hour.) <BR>\n" );
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document.write( "If all the numbers you gave in the problem are correct, this plane is flying in a category 5+ <BR>\n" );
document.write( "hurricane or something similar ... headwinds over 210 miles per hour ... and probably shouldn't <BR>\n" );
document.write( "be up in the air at all.  Its actual speed is its speed in still air (268 miles per hour)<BR>\n" );
document.write( "minus the speed of the wind (210.8 miles per hour) which results in an actual speed of<BR>\n" );
document.write( "57.2 miles per hour relative to somebody on the ground ... That's a major slow down, isn't it?<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to work your way through it. <BR>\n" );
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