document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=520120>Question 520120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train leaves Union Staion for Central Station, 216 km away, at 9:00 am.  One hour later a train leaves Central  Station for Union Station. They will meet at noon.  If the second train had started at 9:00 am, and the first  train at 10:30 am, they would still have met at noon. Find the speed of each train.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #346000 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=346000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A train leaves Union Station for Central Station, 216 km away, at 9:00 am. <BR>\n" );
document.write( "One hour later a train leaves Central Station for Union Station.<BR>\n" );
document.write( " They will meet at noon.<BR>\n" );
document.write( " If the second train had started at 9:00 am, and the first train at 10:30 am, they would still have met at noon.<BR>\n" );
document.write( " Find the speed of each train.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let a = Train A's speed<BR>\n" );
document.write( "Let b = Train B's speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "When they meet, the sum of their distances will equal 216 km<BR>\n" );
document.write( "Write a distance equation for each Scenario<BR>\n" );
document.write( ":<BR>\n" );
document.write( "From the information given for the 1st scenario, travel times:<BR>\n" );
document.write( "a = 3 hrs when they meet,  b = 2 hrs when they meet<BR>\n" );
document.write( "3a + 2b = 216 km<BR>\n" );
document.write( ":<BR>\n" );
document.write( "From the information given for the 2nd scenario, travel times:<BR>\n" );
document.write( "a = 1.5 hrs when they meet,  b = 3 hrs when they meet<BR>\n" );
document.write( "1.5a + 3b = 216 km<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Two equations we can solve<BR>\n" );
document.write( "3a + 2b = 216<BR>\n" );
document.write( "1.5a+3b = 216<BR>\n" );
document.write( "multiply the 2nd equation by 2, subtract the 1st equation<BR>\n" );
document.write( "3a + 6b = 432<BR>\n" );
document.write( "3a + 2b = 216<BR>\n" );
document.write( "---------------subtraction eliminates a, find b<BR>\n" );
document.write( "4b = 216<BR>\n" );
document.write( "b = 216/4<BR>\n" );
document.write( "b = 54 km/h, speed of train B<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find a<BR>\n" );
document.write( "3a + 2b = 216<BR>\n" );
document.write( "3a + 2(54) = 216<BR>\n" );
document.write( "3a = 216 - 108<BR>\n" );
document.write( "3a = 108<BR>\n" );
document.write( "a = 108/3<BR>\n" );
document.write( "a = 36 km/h, speed of train A <BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can check these solutions in both scenario equations.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );