document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=815593>Question 815593</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A freight train leaves the station traveling 30km/hr. One hour later, a passanger train leaves the same station on parellel track at 60km/hr. How far from the station does the passanger train overtake the frieght train? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #491098 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=491098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> s = d / t<BR>\n" );
document.write( "d = s * t<BR>\n" );
document.write( "---<BR>\n" );
document.write( "when the passenger train (p) leaves the station, the cargo train (c) has already traveled one hour:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "when p overtakes c, both trains have traveled the same distance from the station, but c has been traveling 1 hour longer than p.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "c at the overtake:<BR>\n" );
document.write( "d = 30 / t<BR>\n" );
document.write( "where t is the time of the overtake, measured from the time that c departed the station<BR>\n" );
document.write( "---<BR>\n" );
document.write( "p at the overtake:<BR>\n" );
document.write( "d = 60 / (t + 1)<BR>\n" );
document.write( "where t is the time of the overtake, measured from the time that c departed the station<BR>\n" );
document.write( "---<BR>\n" );
document.write( "c and p at the overtake:<BR>\n" );
document.write( "d = 30/t = 60/(t + 1)<BR>\n" );
document.write( "30(t + 1)/(t(t + 1)) = 60t/(t(t + 1))<BR>\n" );
document.write( "60t/(t(t + 1)) - 30(t + 1)/(t(t + 1)) = 0<BR>\n" );
document.write( "60t - 30(t + 1) = 0(t(t + 1))<BR>\n" );
document.write( "60t - 30t - 30 = 0<BR>\n" );
document.write( "30t = 30<BR>\n" );
document.write( "---<BR>\n" );
document.write( "time of the overtake:<BR>\n" );
document.write( "t = 1 hour after c departed the station<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "d = 30 / t<BR>\n" );
document.write( "d = 30 km/hr / 1 hr = 30 km<BR>\n" );
document.write( "so the overtake occurs 30 km from the station<BR>\n" );
document.write( "---<BR>\n" );
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document.write( "---<BR>\n" );
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document.write( "---<BR>\n" );
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document.write( "---<BR>\n" );
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