document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=299160>Question 299160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a plane flew 500 km from atlanta to louisville. when returning to atlanta the flight took 1/2 hour less time.if the rate to Louisville was 50km/hr faster than the rate returning, find the two rates in km/hr. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #215068 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=215068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a plane flew 500 km from atlanta to louisville. when returning to atlanta the flight took 1/2 hour less time.if the rate to Louisville was 50km/hr faster than the rate returning, find the two rates in km/hr.\r<BR>\n" );
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document.write( "let the returning rate be x kmh\r<BR>\n" );
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document.write( "time taken while returning = 500/x\r<BR>\n" );
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document.write( "the rate to louisville will be x+50 mph\r<BR>\n" );
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document.write( "the time taken while going is 500/ x+50\r<BR>\n" );
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document.write( "the distance traveled each way is 500 km\r<BR>\n" );
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document.write( "500/x -500/ x+50 = 1/2\r<BR>\n" );
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document.write( "500(x+50) - 500x= 1/2 * x(x+50)\r<BR>\n" );
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document.write( "500x+25000 -500x = x^2 +50x  /2\r<BR>\n" );
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document.write( "2*500x +2 * 25000 = x^2 +50x\r<BR>\n" );
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document.write( "1000x +50000 = x^2 +50x\r<BR>\n" );
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document.write( "x^2-950x -50000=0\r<BR>\n" );
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document.write( "x^2-1000x+50x-50000=0\r<BR>\n" );
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document.write( "x(x-1000)+50(x-1000)=0\r<BR>\n" );
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document.write( "(x-1000)(x+50)=0\r<BR>\n" );
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document.write( "x=1000 km / hour  returning rate\r<BR>\n" );
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document.write( "1050 km / hr is the going rate to louisville\r<BR>\n" );
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document.write( " </SPAN>\n" );
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