document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=959193>Question 959193</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A goods train leaves a station at 6 p.m. followed by an express train which leaves at 8 p.m and travels 20 km/ hr faster than good train. The express train arrives at a station 1040 km away, 36 min before the goods train. Find their speeds. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #586309 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=586309\">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 of the goods train in km/hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+%2B+20+ ALIGN=MIDDLE  ALT=\"+s+%2B+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the speed of the express train in km/hr<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "From 6 pm to 8 pm, the goods train gets a<BR>\n" );
document.write( "head start of:<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;\" > km<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Start a stopwatch when the express train leaves<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the time on the stopwatch when the <BR>\n" );
document.write( "express train arrives at station.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+%2B+36%2F60+ ALIGN=MIDDLE  ALT=\"+t+%2B+36%2F60+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time on stopwatch when goods train arrives<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Equation for the goods train:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1040+-+2s+=+s%2A%28+t+%2B+36%2F60+%29+ ALIGN=MIDDLE  ALT=\"+1040+-+2s+=+s%2A%28+t+%2B+36%2F60+%29+\"   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=+1040+=+%28+s+%2B+20+%29%2At+ ALIGN=MIDDLE  ALT=\"+1040+=+%28+s+%2B+20+%29%2At+\"   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=+1040+-+2s+=+s%2At+%2B+%28+3%2F5+%29%2As+ ALIGN=MIDDLE  ALT=\"+1040+-+2s+=+s%2At+%2B+%28+3%2F5+%29%2As+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1040+=+s%2A%28+t+%2B+13%2F5+%29+ ALIGN=MIDDLE  ALT=\"+1040+=+s%2A%28+t+%2B+13%2F5+%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=+s+=+1040+%2F+%28+t+%2B+13%2F5+%29+ ALIGN=MIDDLE  ALT=\"+s+=+1040+%2F+%28+t+%2B+13%2F5+%29+\"   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=+1040+=+s%2At+%2B+20t+ ALIGN=MIDDLE  ALT=\"+1040+=+s%2At+%2B+20t+\"   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=+1040+=+%28+1040+%2F+%28+t+%2B+13%2F5+%29%29%2At+%2B+20t+ ALIGN=MIDDLE  ALT=\"+1040+=+%28+1040+%2F+%28+t+%2B+13%2F5+%29%29%2At+%2B+20t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1040%2A%28+t+%2B+13%2F5+%29+=+1040t+%2B+20t%2A%28+t+%2B+13%2F5+%29+ ALIGN=MIDDLE  ALT=\"+1040%2A%28+t+%2B+13%2F5+%29+=+1040t+%2B+20t%2A%28+t+%2B+13%2F5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1040t+%2B+2704+=+1040t+%2B+20t%5E2+%2B+52t+ ALIGN=MIDDLE  ALT=\"+1040t+%2B+2704+=+1040t+%2B+20t%5E2+%2B+52t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20t%5E2+%2B+52t+-+2704+=+0+ ALIGN=MIDDLE  ALT=\"+20t%5E2+%2B+52t+-+2704+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5t%5E2+%2B+13t++-+676+=+0+ ALIGN=MIDDLE  ALT=\"+5t%5E2+%2B+13t++-+676+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a=+5+ ALIGN=MIDDLE  ALT=\"+a=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+13+ ALIGN=MIDDLE  ALT=\"+b+=+13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-676+ ALIGN=MIDDLE  ALT=\"+c+=+-676+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-13+%2B-+sqrt%28+13%5E2+-+4%2A5%2A%28-676%29+%29%29+%2F+%282%2A5%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-13+%2B-+sqrt%28+13%5E2+-+4%2A5%2A%28-676%29+%29%29+%2F+%282%2A5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-13+%2B-+sqrt%28+169+%2B+13520++%29%29+%2F+10+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-13+%2B-+sqrt%28+169+%2B+13520++%29%29+%2F+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-13+%2B-+sqrt%28+13689++%29%29+%2F+10+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-13+%2B-+sqrt%28+13689++%29%29+%2F+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-13+%2B+117+%29+%2F+10+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-13+%2B+117+%29+%2F+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+104%2F10+ ALIGN=MIDDLE  ALT=\"+t+=+104%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+10.4+ ALIGN=MIDDLE  ALT=\"+t+=+10.4+\"   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=+1040+=+%28+s+%2B+20+%29%2At+ ALIGN=MIDDLE  ALT=\"+1040+=+%28+s+%2B+20+%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1040+=+%28+s+%2B+20+%29%2A10.4+ ALIGN=MIDDLE  ALT=\"+1040+=+%28+s+%2B+20+%29%2A10.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100+=+s+%2B+20+ ALIGN=MIDDLE  ALT=\"+100+=+s+%2B+20+\"   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+=+80+ ALIGN=MIDDLE  ALT=\"+s+=+80+\"   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+20+=+100+ ALIGN=MIDDLE  ALT=\"+s+%2B+20+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "The speed of the goods train is 80 km/hr<BR>\n" );
document.write( "The speed of the express train is 100 km/hr<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1040+-+2s+=+s%2A%28+t+%2B+36%2F60+%29+ ALIGN=MIDDLE  ALT=\"+1040+-+2s+=+s%2A%28+t+%2B+36%2F60+%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=+1040+-+2%2A80+=+80%2A%28+10.4+%2B+36%2F60+%29+ ALIGN=MIDDLE  ALT=\"+1040+-+2%2A80+=+80%2A%28+10.4+%2B+36%2F60+%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=+1040+-+160+=+80%2A11+ ALIGN=MIDDLE  ALT=\"+1040+-+160+=+80%2A11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+880+=+880+ ALIGN=MIDDLE  ALT=\"+880+=+880+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );