document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83265>Question 83265</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane flies 720 mi against a steady 30 mi.h headwind and then returns to the same point with the wind. If the entire trip takes 10 hr what is the planes speed in still air?: A plane flies 720 mi against a steady 30 mi.h headwind and then returns to the same point with the wind. If the entire trip takes 10 hr what is the planes speed in still air?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59898 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=59898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let x=speed (rate) of the plane in still air<BR>\n" );
document.write( "speed against headwind =x-30<BR>\n" );
document.write( "speed with headwind=x+30\r<BR>\n" );
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document.write( "Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r\r<BR>\n" );
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document.write( "Time required travelling against the headwind=720/(x-30)<BR>\n" );
document.write( "Time require travelling with the headwind=720/(x+30)\r<BR>\n" );
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document.write( "Now we are told that the total time was 10 hours, So:\r<BR>\n" );
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document.write( "720/(x-30)+720/(x+30)=10  multiply both sides by (x-30)(x+30)\r<BR>\n" );
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document.write( "720(x+30)+720(x-30)=10(x-30)(x+30)  divide both sides by 10\r<BR>\n" );
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document.write( "72(x+30)+72(x-30)=(x-30)(x+30)   get rid of parens\r<BR>\n" );
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document.write( "72x+2160+72x-2160=x^2-900  collect like terms\r<BR>\n" );
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document.write( "144x=x^2-900  subtract 144x from both sides\r<BR>\n" );
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document.write( "144x-144x=x^2-144x-900  simplify\r<BR>\n" );
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document.write( "x^2-144x-900=0   quadratic in standard form and this can be factored\r<BR>\n" );
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document.write( "(x-150)(x+6)=0\r<BR>\n" );
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document.write( "x=150mph-------------------------------------rate in still air<BR>\n" );
document.write( "x=-6----------------discount negative value for speed\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "720/(150-30)+720/(150+30)=10\r<BR>\n" );
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document.write( "6+4=10<BR>\n" );
document.write( "10=10\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
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