document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155059>Question 155059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An express and local train leave Gray’s Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. 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 #114162 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=114162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: The information \" leave Gray’s Lake at 3 P.M\" is extra information that is not helpful. So we can ignore the \"3 pm\"\r<BR>\n" );
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document.write( "Let x = speed of local train \r<BR>\n" );
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document.write( "Let's set up the equation 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 equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50=%28x%29t ALIGN=MIDDLE  ALT=\"50=%28x%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=50 ALIGN=MIDDLE  ALT=\"d=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the distance from the lake to Chicago) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=x ALIGN=MIDDLE  ALT=\"r=x\"   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=50%2Fx=t ALIGN=MIDDLE  ALT=\"50%2Fx=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by \"x\" to solve for \"t\"\r<BR>\n" );
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document.write( "So the time \"t\" can be represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=50%2Fx ALIGN=MIDDLE  ALT=\"t=50%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's set up the equation 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;\" > Go back to the distance-rate-time equation\r<BR>\n" );
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document.write( "Since the \"express travels twice as fast as the local\", this means that the speed of the express train is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph. Also, because the express train \"arrives 1 hour ahead of\" the local train, this means that the time of the express train is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-1 ALIGN=MIDDLE  ALT=\"t-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50=2x%28t-1%29 ALIGN=MIDDLE  ALT=\"50=2x%28t-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=50 ALIGN=MIDDLE  ALT=\"d=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2x ALIGN=MIDDLE  ALT=\"r=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and replace \"t\" with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-1 ALIGN=MIDDLE  ALT=\"t-1\"   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=50=2x%2850%2Fx-1%29 ALIGN=MIDDLE  ALT=\"50=2x%2850%2Fx-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=50%2Fx ALIGN=MIDDLE  ALT=\"t=50%2Fx\"   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=50=2x%2850%2Fx%29-2x%281%29 ALIGN=MIDDLE  ALT=\"50=2x%2850%2Fx%29-2x%281%29\"   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=50=100-2x ALIGN=MIDDLE  ALT=\"50=100-2x\"   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=-50=-2x ALIGN=MIDDLE  ALT=\"-50=-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 100 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=x ALIGN=MIDDLE  ALT=\"25=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -2 to isolate \"x\"\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=25 ALIGN=MIDDLE  ALT=\"x=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the speed of the local train is 25 mph and the speed of the express train is 50 mph (since it is twice the speed of the local train)<BR>\n" );
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