document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=407634>Question 407634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes a freight train 3 hours more to travel 200 miles than it takes an express train to travel 120 miles. The rate of the express is 20 miles per hour faster than the rate of the freight train. How do I find the rates of both trains. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287316 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=287316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"The rate of the express is 20 miles per hour faster than the rate of the freight train\"<BR>\n" );
document.write( "___ e = f + 20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t = d / r ___ the freight train time is 3 hr longer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(200 / f) - 3 = 120 / e\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substituting ___ (200 / f) - 3 = [120 / (f + 20)]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiplying by [f(f+20)] ___ 200(f+20) - 3[f(f+20)] = 120(f)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "200f + 4000 - 3f^2 - 60f = 120f ___ 0 = 3f^2 - 20f - 4000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factoring ___ 0 = (3f + 100)(f - 40)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3f + 100 = 0 ___ f = -100/3 ___ negative value not realistic\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f - 40 = 0 ___ f = 40 ___ substitute back to find e </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );