document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=648831>Question 648831</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Train Speed: A train leaves Los Angeles at 2:00 PM. A second train leaves the same station in the same direction at 4:00 PM. The second train travels 24 mph faster than the first. If the second train overtakes the first at 7:00 PM, what is the speed of each of the two trains? \r<BR>\n" );
document.write( "\n" );
document.write( "I am not sure how to construct an equation to solve this problem.<BR>\n" );
document.write( "Thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406842 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=406842\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the speed of the 1st train = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+%2B+24+ ALIGN=MIDDLE  ALT=\"+s+%2B+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the speed of the 2nd train<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B1%5D+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the head start  that the 1st train got<BR>\n" );
document.write( "4 PM - 2PM is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B1%5D+=+s%2A2+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+s%2A2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the distance that the 2nd train has to go<BR>\n" );
document.write( "to catch the 1st train<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "7PM - 4PM = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+ ALIGN=MIDDLE  ALT=\"+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "Use this time for both trains. Figure that<BR>\n" );
document.write( "the 1st train already has the head start<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "1st train's equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+-+d%5B1%5D+=+s%2A3+ ALIGN=MIDDLE  ALT=\"+d+-+d%5B1%5D+=+s%2A3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+-+2s+=+s%2A3+ ALIGN=MIDDLE  ALT=\"+d+-+2s+=+s%2A3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "2nd train's equation:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%28+s+%2B+24+%29%2A3+ ALIGN=MIDDLE  ALT=\"+d+=+%28+s+%2B+24+%29%2A3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+5s+ ALIGN=MIDDLE  ALT=\"+d+=+5s+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+3s+%2B+72+ ALIGN=MIDDLE  ALT=\"+d+=+3s+%2B+72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Substitute (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5s+=+3s+%2B+72+ ALIGN=MIDDLE  ALT=\"+5s+=+3s+%2B+72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2s+=+72+ ALIGN=MIDDLE  ALT=\"+2s+=+72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+36+ ALIGN=MIDDLE  ALT=\"+s+=+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "also<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+%2B+24+=+36+%2B+24+ ALIGN=MIDDLE  ALT=\"+s+%2B+24+=+36+%2B+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+%2B+24+=+60+ ALIGN=MIDDLE  ALT=\"+s+%2B+24+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The 1st train's speed is 36 mi/hr<BR>\n" );
document.write( "The 2nd train's speed is 60 mi/hr<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B1%5D+=+s%2A2+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+s%2A2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B1%5D+=+36%2A2+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+36%2A2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B1%5D+=+72+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the 1st train had a head start of 72 mi<BR>\n" );
document.write( "which took 2 hrs. Now it has 3 hrs to go<BR>\n" );
document.write( "the rest of the way<BR>\n" );
document.write( "2nd train's equation:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%28+s+%2B+24+%29%2A3+ ALIGN=MIDDLE  ALT=\"+d+=+%28+s+%2B+24+%29%2A3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+60%2A3+ ALIGN=MIDDLE  ALT=\"+d+=+60%2A3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+180+ ALIGN=MIDDLE  ALT=\"+d+=+180+\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180+-+72+=+108+ ALIGN=MIDDLE  ALT=\"+180+-+72+=+108+\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "The 1st train must go 108 mi in 3 hrs at 36 mi/hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+108+=+36%2A3+ ALIGN=MIDDLE  ALT=\"+108+=+36%2A3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+108+=+108+ ALIGN=MIDDLE  ALT=\"+108+=+108+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( " </SPAN>\n" );
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