document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=834503>Question 834503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that a plane is traveling at a constant speed under unvarying wind conditions. Traveling agaisnt a headwind, the plane takes 4 hours to travel 1540 miles. Traveling with a tail wind, the plane flies 1365 miles in 3 hours. Find the speed of the plane and 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 #503047 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=503047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You probably meant to ask for the solution further down below, starting at \"WHAT did you really mean to describe?\"-------------\r<BR>\n" );
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document.write( "H = speed of plane chosen without wind but during travel opposing the wind<BR>\n" );
document.write( "L = speed of plane chosen without wind but during travel along or with the wind<BR>\n" );
document.write( "w = speed of wind\r<BR>\n" );
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document.write( "Note that I am taking your wording, \"Assume that a plane is traveling at a constant speed under unvarying wind conditions\" exactly as written.  That means the plane travel is the same speed in both directions.  YOU HAVE THREE VARIABLES.\r<BR>\n" );
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document.write( "______________speed______________time___________distance<BR>\n" );
document.write( "AGAINST W_____H-w________________4______________1540<BR>\n" );
document.write( "WITH W________L+w________________3______________1365\r<BR>\n" );
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document.write( "Further, as stated in the description, if speed is constant for both directions then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H-w=L%2Bw ALIGN=MIDDLE  ALT=\"H-w=L%2Bw\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28H-L=2w%29 ALIGN=MIDDLE  ALT=\"highlight_green%28H-L=2w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;\r<BR>\n" );
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document.write( "We can make two more equations based on the data table shown above:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28H-w%29%2A4=1540 ALIGN=MIDDLE  ALT=\"%28H-w%29%2A4=1540\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%2Bw%29%2A3=1365 ALIGN=MIDDLE  ALT=\"%28L%2Bw%29%2A3=1365\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which now give a system of three equations in three unknowns.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28H-w%29%2A4=1540 ALIGN=MIDDLE  ALT=\"%28H-w%29%2A4=1540\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H-w=385 ALIGN=MIDDLE  ALT=\"H-w=385\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(L+w)*3=1365<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2Bw=455 ALIGN=MIDDLE  ALT=\"L%2Bw=455\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The system can be expressed in these simultaneous equations:<BR>\n" );
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document.write( "H-L=2w<BR>\n" );
document.write( "H-w=385<BR>\n" );
document.write( "L+w=455<BR>\n" );
document.write( "-----------\r<BR>\n" );
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document.write( "Try eliminating for w to get two equations in H and L.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28H-L%29%2F2 ALIGN=MIDDLE  ALT=\"w=%28H-L%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H-%28H-L%29%2F2=385 ALIGN=MIDDLE  ALT=\"H-%28H-L%29%2F2=385\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H-H%2F2%2BL%2F2=385 ALIGN=MIDDLE  ALT=\"H-H%2F2%2BL%2F2=385\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%2F2%2BL%2F2=385 ALIGN=MIDDLE  ALT=\"H%2F2%2BL%2F2=385\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%2BL=770 ALIGN=MIDDLE  ALT=\"H%2BL=770\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "L+(H-L)/2=455<BR>\n" );
document.write( "2L+H-L=2*455<BR>\n" );
document.write( "2L+H-L=910<BR>\n" );
document.write( "H+L=910<BR>\n" );
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document.write( "NO GOOD.  H+L cannot be both 910 and 770 at the same time.  \r<BR>\n" );
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document.write( "WHAT did you really mean to describe?  Did you mean, \"both planes travel at constant, but DIFFERENT speeds in each direction\"?  If THAT is really what you mean, then just assume the plane has a speed r without wind, and try this data arrangement:\r<BR>\n" );
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document.write( "Regarding Winde_______speed____________time____________distance<BR>\n" );
document.write( "AGAINST_______________r-w______________4_______________1540<BR>\n" );
document.write( "WITH__________________r+w______________3_______________1365\r<BR>\n" );
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document.write( "TWO EQUATIONS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r-w%29%2A4=1540 ALIGN=MIDDLE  ALT=\"%28r-w%29%2A4=1540\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r-w%29=385 ALIGN=MIDDLE  ALT=\"%28r-w%29=385\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-w=385 ALIGN=MIDDLE  ALT=\"r-w=385\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2Bw%29%2A3=1365 ALIGN=MIDDLE  ALT=\"%28r%2Bw%29%2A3=1365\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Bw=455 ALIGN=MIDDLE  ALT=\"r%2Bw=455\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "SYSTEM TO SOLVE READY TO SOLVE:<BR>\n" );
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document.write( "r-w=385<BR>\n" );
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document.write( "r+w=455<BR>\n" );
document.write( "-----------------\r<BR>\n" );
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document.write( "Add the left members and add the right members and this eliminates w for getting a value for r.<BR>\n" );
document.write( "This produces first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r=840 ALIGN=MIDDLE  ALT=\"2r=840\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=420%29 ALIGN=MIDDLE  ALT=\"highlight%28r=420%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use either equation of the system to get the value for w.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Bw=455 ALIGN=MIDDLE  ALT=\"r%2Bw=455\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=455-r ALIGN=MIDDLE  ALT=\"w=455-r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=455-420 ALIGN=MIDDLE  ALT=\"w=455-420\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=35%29 ALIGN=MIDDLE  ALT=\"highlight%28w=35%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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