document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72815>Question 72815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A light plane flies for 2h with a 20km/h tail wind. The return trip against the same wind takes 3h. Write equations to determine the speed of the plane when there is no wind and the distance travelled </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52156 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=52156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a classic type of problem that uses the equation:<BR>\n" );
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document.write( "Distance = Rate * Time<BR>\n" );
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document.write( "or <BR>\n" );
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document.write( "D= R*T <BR>\n" );
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document.write( "for short.<BR>\n" );
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document.write( "All you have to figure out is what to put into the equation.<BR>\n" );
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document.write( "You are told that on one leg of a trip a plane flies for 2 hours (that means T = 2) and it <BR>\n" );
document.write( "has a tail wind of 20 km per hour.  Therefore the rate that it is going at is the speed of <BR>\n" );
document.write( "the airplane (call it S) + 20 km per hour that the wind is pushing it. This rate can be <BR>\n" );
document.write( "written as (S+20).<BR>\n" );
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document.write( "So on this leg of the trip the distance traveled is given by the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+%28S%2B20%29%2A2+=+2S+%2B+40 ALIGN=MIDDLE  ALT=\"D+=+%28S%2B20%29%2A2+=+2S+%2B+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the return home the plane flies for 3 hours so T = 3.  But this time instead of boosting<BR>\n" );
document.write( "the plane's speed the wind is slowing the plane down because the plane is flying into the wind.<BR>\n" );
document.write( "So this time the rate at which the plane is flying is (S - 20) which is the speed of the<BR>\n" );
document.write( "plane minus the speed of the wind. So the distance equation for the trip back home can<BR>\n" );
document.write( "be written as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+%28S-20%29%2A3 ALIGN=MIDDLE  ALT=\"D+=+%28S-20%29%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But in both cases the distance covered is the same amount.  Therefore the right sides of<BR>\n" );
document.write( "these two equations have to be equal.  This equality can be written as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28S%2B20%29%2A2+=+%28S-20%29%2A3 ALIGN=MIDDLE  ALT=\"%28S%2B20%29%2A2+=+%28S-20%29%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply both sides out to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2S%2B40+=+3S-60 ALIGN=MIDDLE  ALT=\"2S%2B40+=+3S-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 3S from both sides to eliminate the 3S on the right side.  The result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-S+%2B+40+=+-60 ALIGN=MIDDLE  ALT=\"-S+%2B+40+=+-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 40 from both sides to get rid of the +40 on the left side.  When you do the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-S+=+-100 ALIGN=MIDDLE  ALT=\"-S+=+-100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And as a final step multiply both sides by -1 to get that S, the speed of the plane in<BR>\n" );
document.write( "still air is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+100+km%2Fhr ALIGN=MIDDLE  ALT=\"S+=+100+km%2Fhr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So we have that the speed of the plane is 100 km/hr.  When the wind pushes the plane it<BR>\n" );
document.write( "boosts the speed of the plane by 20 km/hr so the plane is going 120 km/hr and it goes at<BR>\n" );
document.write( "that speed for 2 hours.  So multiplying the rate times the time gives us:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2A2+=+240 ALIGN=MIDDLE  ALT=\"120%2A2+=+240\"   DISABLED_style= \"max-width:90%; height:auto;\" > km<BR>\n" );
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document.write( "For grins, let's check the flight back home.  This time the plane is flying at the speed<BR>\n" );
document.write( "it would be at in still or calm air (100 km/hr) but because it is going into a 20 km/hr head <BR>\n" );
document.write( "wind it is slowed to 100-20 = 80 km/hr.  So it's true ground speed is 80 km/hr and it flies<BR>\n" );
document.write( "this leg for 3 hrs before it gets home.  Using the distance formula, the distance covered<BR>\n" );
document.write( "is this rate times the time of 3 hrs or:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+80%2A3+=+240 ALIGN=MIDDLE  ALT=\"D+=+80%2A3+=+240\"   DISABLED_style= \"max-width:90%; height:auto;\" > km.  <BR>\n" );
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document.write( "The problem checks out because the distance is the same amount both going and coming.<BR>\n" );
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document.write( "Note that this plane is not very fast.  In still air it flies at about 62 miles per hour,<BR>\n" );
document.write( "and even with a 20 km/hr tail wind pushing it it is only going about 72 miles per hour.<BR>\n" );
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document.write( "Hope this helps you to understand the basics of this problem.  The most difficult thing<BR>\n" );
document.write( "about the problem is determining what the words are telling you about the performance<BR>\n" );
document.write( "of the plane relative to the wind. </SPAN>\n" );
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