document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237015>Question 237015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An express train and a local train leave Grays Lake at 3:00 P.M. and head for Chicago 50 miles away.  The express travels twice as fast as the local and arrivies 1 hour ahead of the local.  Find the speed of each train algebraically and show work.  I believe the speed of the trains is 40 and 20 miles per hour respectivelly.. I'm having trouble formulating the equations<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 #174355 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "First let's test your theory.\r<BR>\n" );
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document.write( "We know that distance equals rate times time, or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\ =\ rt\">,\r<BR>\n" );
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document.write( "So if the express train went 50 miles at 40 miles per hour, it would have taken <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{50}{40}\ =\ 1.25\"> hours.  And it would have taken the local train @ 20mph <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{50}{20}\ =\ 2.5\"> hours.  That means that the express train would have arrived an hour and 15 minutes ahead of the local, not 1 hour like the problem states.  [BUZZZ!!!] Thank you for playing, we have some lovely parting gifts...\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> represent the rate of the local train.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2r\"> must be the rate of the express train.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> be the time it took the local train, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\ -\ 1\"> is the time it took the express train.  The distance is the same 50 miles for both trains, so:\r<BR>\n" );
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document.write( "For the local train:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 50\ =\ rt\">\r<BR>\n" );
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document.write( "For the express:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \,50\ =\ 2r(t\ -\ 1)\">\r<BR>\n" );
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document.write( "Multiply both sides of the first equation by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{r}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \,t\ =\ \frac{50}{r}\">\r<BR>\n" );
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document.write( "Multiply both sides of the second equation by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{2r}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ -\ 1\ =\ \frac{50}{2r}\ =\ \frac{25}{r}\">\r<BR>\n" );
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document.write( "Add 1 to both sides of the second equation and combine using the LCD of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{25\ +\ r}{r}\">\r<BR>\n" );
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document.write( "Now we have two expressions for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\"> in terms of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r\">.  Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\ =\ t\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{50}{r}\ =\ \frac{25\ +\ r}{r}\">\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{r}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25\ +\ r\ =\ 50\">\r<BR>\n" );
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document.write( "I'll let you take it from there.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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