document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82011>Question 82011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the speed of an airplane in still air is 224km/h. the plane travels 716 km against the wind and 1904 km with the wind in a total time of 12 hr. 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 #58808 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=58808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> distance(d)=rate(r) times time(t) or d=rt;t=d/r and r=d/t\r<BR>\n" );
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document.write( "Let r=speed of the wind\r<BR>\n" );
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document.write( "time airplane traveled against the wind=716/(224-r)<BR>\n" );
document.write( "time airplane traveled with the wind =1904/(224+r)\r<BR>\n" );
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document.write( "Now we are told that the sum of these times is 12 hrs.  So:\r<BR>\n" );
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document.write( "716/(224-r)+1904/(224+r)=12  multiply each term by (224-r)(224+r) to get rid of fractions:\r<BR>\n" );
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document.write( "716(224-r)(224+r)/(224-r)+1904(224-r)(224+r)/(224+r)=12(224-r)(224+r) simplify:\r<BR>\n" );
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document.write( "716(224+r)+1904(224-r)=12((224-r)(224+r)  get rid of parens\r<BR>\n" );
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document.write( "160384+716r+426496-1904r=602112-12r^2  simplify\r<BR>\n" );
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document.write( "586880-1188r=602112-12r^2  subtract 602112 and add 12r^2 to both sides\r<BR>\n" );
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document.write( "12r^2-1188r-15232=0  divide each term by 4\r<BR>\n" );
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document.write( "3r^2-297r-3808=0  quadratic in standard form.  Solve using quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28297+%2B-+sqrt%28+297%5E2-4%2A3%2A%28-3808%29+%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"x+=+%28297+%2B-+sqrt%28+297%5E2-4%2A3%2A%28-3808%29+%29%29%2F%282%2A3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28297+%2B-+sqrt%28133905%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"x+=+%28297+%2B-+sqrt%28133905%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28297+%2B-+365.930%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"x+=+%28297+%2B-+365.930%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=110.4883 ALIGN=MIDDLE  ALT=\"x=110.4883\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph----------------------speed of the wind\r<BR>\n" );
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document.write( "discount the negative value of x\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "716/(224-110.4883)+1904/(224+110.4883)=12<BR>\n" );
document.write( "716/(113.5116)+1904/(334.4883)=12<BR>\n" );
document.write( "6.3077+5.6923=12<BR>\n" );
document.write( "~12=12\r<BR>\n" );
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document.write( "----a nasty problem with respect to manipulating the terms---there may be an easier way, but I don't see it.  It's good that we have calculators!\r<BR>\n" );
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document.write( "Hope this helps----ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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