document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199079>Question 199079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.	An express train and a local train both leave Gray’s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it.  Find the speed of each train. \r<BR>\n" );
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document.write( "I am confused by this problem and do not know where to start. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149533 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=149533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D ALIGN=MIDDLE  ALT=\"t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time of express train and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D ALIGN=MIDDLE  ALT=\"t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time of local train\r<BR>\n" );
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document.write( "Also, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D ALIGN=MIDDLE  ALT=\"r%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = speed of express train and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D ALIGN=MIDDLE  ALT=\"r%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = speed of local train\r<BR>\n" );
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document.write( "Since the \"express train travels twice as fast as the local train\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D=2%2Ar%5B2%5D ALIGN=MIDDLE  ALT=\"r%5B1%5D=2%2Ar%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, because \"the express train arrives 2 hours ahead of the local train\", this tells us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D=t%5B2%5D-2 ALIGN=MIDDLE  ALT=\"t%5B1%5D=t%5B2%5D-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's set up the formula for the local train:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the distance rate time formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=r%5B2%5D%2At%5B2%5D ALIGN=MIDDLE  ALT=\"60=r%5B2%5D%2At%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=60 ALIGN=MIDDLE  ALT=\"d=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=r%5B2%5D ALIGN=MIDDLE  ALT=\"r=r%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=t%5B2%5D ALIGN=MIDDLE  ALT=\"t=t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Ft%5B2%5D=r%5B2%5D ALIGN=MIDDLE  ALT=\"60%2Ft%5B2%5D=r%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D ALIGN=MIDDLE  ALT=\"t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So after isolating the second speed, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D=60%2Ft%5B2%5D ALIGN=MIDDLE  ALT=\"r%5B2%5D=60%2Ft%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's set up the formula for the express train:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the distance rate time formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=r%5B1%5D%2At%5B1%5D ALIGN=MIDDLE  ALT=\"60=r%5B1%5D%2At%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=60 ALIGN=MIDDLE  ALT=\"d=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=r%5B1%5D ALIGN=MIDDLE  ALT=\"r=r%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=t%5B1%5D ALIGN=MIDDLE  ALT=\"t=t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=%282%2Ar%5B2%5D%29%2A%28t%5B2%5D-2%29 ALIGN=MIDDLE  ALT=\"60=%282%2Ar%5B2%5D%29%2A%28t%5B2%5D-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D=2%2Ar%5B2%5D ALIGN=MIDDLE  ALT=\"r%5B1%5D=2%2Ar%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D=t%5B2%5D-2 ALIGN=MIDDLE  ALT=\"t%5B1%5D=t%5B2%5D-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=%282%2A%2860%2Ft%5B2%5D%29%29%2A%28t%5B2%5D-2%29 ALIGN=MIDDLE  ALT=\"60=%282%2A%2860%2Ft%5B2%5D%29%29%2A%28t%5B2%5D-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D=60%2Ft%5B2%5D ALIGN=MIDDLE  ALT=\"r%5B2%5D=60%2Ft%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=%28120%2Ft%5B2%5D%29%2A%28t%5B2%5D-2%29 ALIGN=MIDDLE  ALT=\"60=%28120%2Ft%5B2%5D%29%2A%28t%5B2%5D-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60t%5B2%5D=120%28t%5B2%5D-2%29 ALIGN=MIDDLE  ALT=\"60t%5B2%5D=120%28t%5B2%5D-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D ALIGN=MIDDLE  ALT=\"t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60t%5B2%5D=120t%5B2%5D-240 ALIGN=MIDDLE  ALT=\"60t%5B2%5D=120t%5B2%5D-240\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60t%5B2%5D-120t%5B2%5D=-240 ALIGN=MIDDLE  ALT=\"60t%5B2%5D-120t%5B2%5D=-240\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120t%5B2%5D ALIGN=MIDDLE  ALT=\"120t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-60t%5B2%5D=-240 ALIGN=MIDDLE  ALT=\"-60t%5B2%5D=-240\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D=-240%2F%28-60%29 ALIGN=MIDDLE  ALT=\"t%5B2%5D=-240%2F%28-60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -60 to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D ALIGN=MIDDLE  ALT=\"t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D=4 ALIGN=MIDDLE  ALT=\"t%5B2%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So it takes 4 hours for the local train\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=r%5B2%5D%2At%5B2%5D ALIGN=MIDDLE  ALT=\"60=r%5B2%5D%2At%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the local train formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=r%5B2%5D%2A4 ALIGN=MIDDLE  ALT=\"60=r%5B2%5D%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D=4 ALIGN=MIDDLE  ALT=\"t%5B2%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F4=r%5B2%5D ALIGN=MIDDLE  ALT=\"60%2F4=r%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15=r%5B2%5D ALIGN=MIDDLE  ALT=\"15=r%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide.\r<BR>\n" );
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document.write( "So the speed of the local train is 15 mph\r<BR>\n" );
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document.write( "Now simply double the speed of the local train to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A2=30 ALIGN=MIDDLE  ALT=\"15%2A2=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the speed of the local train is 15 mph and the speed of the express train is 30 mph. \r<BR>\n" );
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document.write( "Note: nowhere in the solution above is a mention of 12:00 noon. This information is unnecessary and it is put in there to throw you off. </SPAN>\n" );
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