document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020503>Question 1020503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the average speed of the local train is 10 miles per hour less than two-thirds the speed of the express train. the local train leaves at noon. the express train leaves at 1:00 pm, from the same station and travels in the same direction as the local train on a parallel track. if the express train overtakes the local train at 2:00 pm, what is 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 #636422 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=636422\">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=+s+ ALIGN=MIDDLE  ALT=\"+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the speed in mi/hr of the express train<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%2F3%29%2As+-+10+ ALIGN=MIDDLE  ALT=\"+%282%2F3%29%2As+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the speed of the local train<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "From noon to 1 PM is 1 hr. How much of a headstart<BR>\n" );
document.write( "in miles does the local train have?<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B1%5D+=+%28%282%2F3%29%2As+-+10+%29%2A1+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+%28%282%2F3%29%2As+-+10+%29%2A1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Time both trains starting at 1 PM to 2 PM<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 in miles the express train travels<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Equation for local train:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+-+%28%282%2F3%29%2As+-+10+%29+=+%28%282%2F3%29%2As+-+10+%29%2A1+ ALIGN=MIDDLE  ALT=\"+d+-+%28%282%2F3%29%2As+-+10+%29+=+%28%282%2F3%29%2As+-+10+%29%2A1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation for express train:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+s%2A1+ ALIGN=MIDDLE  ALT=\"+d+=+s%2A1+\"   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+=+2%2A%28+%282%2F3%29%2As+-+10+%29+ ALIGN=MIDDLE  ALT=\"+d+=+2%2A%28+%282%2F3%29%2As+-+10+%29+\"   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+=+%284%2F3%29%2As+-+20+ ALIGN=MIDDLE  ALT=\"+d+=+%284%2F3%29%2As+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute (2) into (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%284%2F3%29%2As+-+20+ ALIGN=MIDDLE  ALT=\"s+=+%284%2F3%29%2As+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3s+=+4s+-+60+ ALIGN=MIDDLE  ALT=\"+3s+=+4s+-+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+60+ ALIGN=MIDDLE  ALT=\"+s+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%2F3%29%2As+-+10+=+%282%2F3%29%2A60+-+10+ ALIGN=MIDDLE  ALT=\"+%282%2F3%29%2As+-+10+=+%282%2F3%29%2A60+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%2F3%29%2As+-+10+=+40+-+10+ ALIGN=MIDDLE  ALT=\"+%282%2F3%29%2As+-+10+=+40+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%2F3%29%2As+-+10+=+30+ ALIGN=MIDDLE  ALT=\"+%282%2F3%29%2As+-+10+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "The local train's speed is 30 mi/hr<BR>\n" );
document.write( "The express train's speed is 60 mi/hr<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B1%5D+=+%28%282%2F3%29%2As+-+10+%29%2A1+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+%28%282%2F3%29%2As+-+10+%29%2A1+\"   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+=+%28%282%2F3%29%2As+-+10+%29%2A1+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+%28%282%2F3%29%2As+-+10+%29%2A1+\"   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+=+30+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+30+\"   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+-+%28%282%2F3%29%2As+-+10+%29+=+%28%282%2F3%29%2As+-+10+%29%2A1+%0D%0A%281%29+%7B%7B%7B+d+-+30+=+30+ ALIGN=MIDDLE   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+=+60+ ALIGN=MIDDLE  ALT=\"+d+=+60+\"   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+=+s%2A1+ ALIGN=MIDDLE  ALT=\"+d+=+s%2A1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+60+=+s+ ALIGN=MIDDLE  ALT=\"+60+=+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );