document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636847>Question 636847</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The distance between train station A and train station B is 180 kilometers. Train station C is between station A and station B, and is located 30 kilometers away from station A. At 7 AM, a freight train left from station A to station B and at 8 AM, a passenger train left from station C to station B. The speed of the passenger train is 30 km/hour greater than the freight train. <BR>\n" );
document.write( "The passenger train arrived to station B 20 minutes earlier than the freight train arrived to station B.<BR>\n" );
document.write( "What is the speed of the freight train?<BR>\n" );
document.write( "Thanks so much for your time! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401254 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=401254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The distance between train station A and train station B is 180 kilometers. Train station C is between station A and station B, and is located 30 kilometers away from station A.<BR>\n" );
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document.write( "Draw that picture:<BR>\n" );
document.write( "30 km from A to C<BR>\n" );
document.write( "180 km from A to B<BR>\n" );
document.write( "150 km from C to B<BR>\n" );
document.write( "A......30km.....C.............130km......B\r<BR>\n" );
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document.write( " At 7 AM, a freight train left from station A to station B and at 8 AM, a passenger train left from station C to station B. The speed of the passenger train is 30 km/hour greater than the freight train. <BR>\n" );
document.write( "The passenger train arrived to station B 20 minutes earlier than the freight train arrived to station B.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Freight DATA:<BR>\n" );
document.write( "rate = x kmh ; distance = 180 km ; time = d/r = 180/(x) hrs<BR>\n" );
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document.write( "Passenger DATA:<BR>\n" );
document.write( "rate = x+30 kmh ; distance = 130 km ; time = d/r = 130/(x+30) hrs<BR>\n" );
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document.write( "What is the speed of the freight train?<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "freight - pass = 1/3 hr<BR>\n" );
document.write( "180/x - 130/(x+30) = 1/3<BR>\n" );
document.write( "----<BR>\n" );
document.write( "3*180(x+30) - 3*130x= x(x+30)<BR>\n" );
document.write( "540x + 16200 - 390x = x^2+30x<BR>\n" );
document.write( "x^2 - 120x - 16200 = 0<BR>\n" );
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document.write( "x = 200 kmh (freight rate)<BR>\n" );
document.write( "x+30 = 230 kmh (passenger rate)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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