document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5092>Question 5092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I know that this motion problem involves a system of  two equations and I could solve it if I could only figure out how to set it up correctly.  I have been using the Distance = Rate x Time formula to try and set it up, but I just can't figure it out and it's driving me nuts!  Here's the problem:\r<BR>\n" );
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document.write( "\"An express train and a local train leave Gray's Lake at 3PM and head for Chicago 50 miles away.  The express travels twice as fast as the local and arrives 1 hour ahead of the local.  Find the speed of each train.\"\r<BR>\n" );
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document.write( "Here's what I've tried to do to set this up.  I've tried to set up a table so I can see what my equations should be.  I'll try to approximate below.\r<BR>\n" );
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document.write( "Using the Rate x Time = Distance formula.  Let s=The speed the train is traveling and let t=the time that it takes to get to Chicago.\r<BR>\n" );
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document.write( "        Rate  Time   Distance<BR>\n" );
document.write( "Local     s  x  t     =50<BR>\n" );
document.write( "Express  2(s)x  t-1   =50\r<BR>\n" );
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document.write( "The above is as far as I get, but I don't think it's right and thus won't get me to the speed that each train is traveling at.\r<BR>\n" );
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document.write( "Help!\r<BR>\n" );
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document.write( "Karen Henry\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2568 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2568\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think your mistake is not putting parentheses around the time (t-1).\r<BR>\n" );
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document.write( "As you said, <BR>\n" );
document.write( "let s = speed of the local<BR>\n" );
document.write( "2s = speed of the express\r<BR>\n" );
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document.write( "t= time of the local<BR>\n" );
document.write( "t-1 = time of the express\r<BR>\n" );
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document.write( "Distances are equal at 50 miles, so (rate times time) = (rate times time)\r<BR>\n" );
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document.write( "s*(t) = 2s *(t-1)\r<BR>\n" );
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document.write( "Since s the speed of the train does not equal zero, you can divide both sides by s:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28s%2At%29%2Fs+=+%282s+%2A+%28t-1%29%29%2Fs+ ALIGN=MIDDLE  ALT=\"+%28s%2At%29%2Fs+=+%282s+%2A+%28t-1%29%29%2Fs+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "t= 2(t-1)<BR>\n" );
document.write( "t=2t -2<BR>\n" );
document.write( "-t = -2<BR>\n" );
document.write( "t=2 hours for the local<BR>\n" );
document.write( "t-1 = 1 hour for the express\r<BR>\n" );
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document.write( "After you do that, then remember that D=RT, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=+D%2FT ALIGN=MIDDLE  ALT=\"R=+D%2FT\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Rate for the local = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2F2 ALIGN=MIDDLE  ALT=\"50%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=25 mph<BR>\n" );
document.write( "Rate for the express = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2F1 ALIGN=MIDDLE  ALT=\"50%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 50 mph.\r<BR>\n" );
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document.write( "R^2 at SCC\r<BR>\n" );
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