document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=628981>Question 628981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A freight train made two 180 km  trips. It made the second trip in 3 hours less time by increasing the rate of travel by 10km/h. Find each rate at which the train left.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395954 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=395954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1st trip:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+r%2At+ ALIGN=MIDDLE  ALT=\"+d+=+r%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180+=+r%2At+ ALIGN=MIDDLE  ALT=\"+180+=+r%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2nd trip:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180+=+%28+r+%2B+10+%29%2A%28+t+-+3+%29+ ALIGN=MIDDLE  ALT=\"+180+=+%28+r+%2B+10+%29%2A%28+t+-+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180+=+r%2At+%2B+10t+-+3r+-+30+ ALIGN=MIDDLE  ALT=\"+180+=+r%2At+%2B+10t+-+3r+-+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+180%2Ft+ ALIGN=MIDDLE  ALT=\"+r+=+180%2Ft+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=+180+=+%28180%2Ft%29%2At+%2B+10t+-+3%2A%28180%2Ft%29+-+30+ ALIGN=MIDDLE  ALT=\"+180+=+%28180%2Ft%29%2At+%2B+10t+-+3%2A%28180%2Ft%29+-+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180+=+180+%2B+10t+-+3%2A%28180%2Ft%29+-+30+ ALIGN=MIDDLE  ALT=\"+180+=+180+%2B+10t+-+3%2A%28180%2Ft%29+-+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=++%2B+10t+-+3%2A%28180%2Ft%29+-+30+ ALIGN=MIDDLE  ALT=\"+0+=++%2B+10t+-+3%2A%28180%2Ft%29+-+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+=+10t+-+3%2A%28180%2Ft%29+ ALIGN=MIDDLE  ALT=\"+30+=+10t+-+3%2A%28180%2Ft%29+\"   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=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30t+=+10t%5E2+-+540+ ALIGN=MIDDLE  ALT=\"+30t+=+10t%5E2+-+540+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10t%5E2+-+30t+-+540+=+0+ ALIGN=MIDDLE  ALT=\"+10t%5E2+-+30t+-+540+=+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=+t%5E2+-+3t+-+54+=+0+ ALIGN=MIDDLE  ALT=\"+t%5E2+-+3t+-+54+=+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=+%28+t+-+9+%29%2A%28+t+%2B+6+%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28+t+-+9+%29%2A%28+t+%2B+6+%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be positive, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+9+ ALIGN=MIDDLE  ALT=\"+t+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the answer<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180+=+r%2At+ ALIGN=MIDDLE  ALT=\"+180+=+r%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180+=+r%2A9+ ALIGN=MIDDLE  ALT=\"+180+=+r%2A9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+180%2F9+ ALIGN=MIDDLE  ALT=\"+r+=+180%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+20+ ALIGN=MIDDLE  ALT=\"+r+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+%2B+10+=+30+ ALIGN=MIDDLE  ALT=\"+r+%2B+10+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The rate for the 1st trip was 20 km/hr<BR>\n" );
document.write( "The rate for the 2nd trip was 30 km/hr<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180+=+%28+r+%2B+10+%29%2A%28+t+-+3+%29+ ALIGN=MIDDLE  ALT=\"+180+=+%28+r+%2B+10+%29%2A%28+t+-+3+%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=+180+=+%28+20+%2B+10+%29%2A%28+9+-+3+%29+ ALIGN=MIDDLE  ALT=\"+180+=+%28+20+%2B+10+%29%2A%28+9+-+3+%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=+180+=+30%2A6+ ALIGN=MIDDLE  ALT=\"+180+=+30%2A6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180+=+180+ ALIGN=MIDDLE  ALT=\"+180+=+180+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );