document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=691629>Question 691629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train runs 224km between 2 cities. If the speed on the way back is 8km/h slower, the run takes half an hour longer. Determine the speed on the way back. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #426786 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=426786\">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=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time in hrs for 1st trip<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+%2B+.5+ ALIGN=MIDDLE  ALT=\"+t+%2B+.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time in hrs for 2nd trip<BR>\n" );
document.write( "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;\" > = speed in km/hr for 1st trip<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+-+8+ ALIGN=MIDDLE  ALT=\"+s+-+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = speed in km/hr for 2nd trip<BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "1st trip:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+224+=+s%2At+ ALIGN=MIDDLE  ALT=\"+224+=+s%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=+224+=+%28+s+-+8+%29%2A%28+t+%2B+.5+%29+ ALIGN=MIDDLE  ALT=\"+224+=+%28+s+-+8+%29%2A%28+t+%2B+.5+%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=+224+=+s%2At+-+8t+%2B+.5s+-+4+ ALIGN=MIDDLE  ALT=\"+224+=+s%2At+-+8t+%2B+.5s+-+4+\"   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=+t+=+224%2Fs+ ALIGN=MIDDLE  ALT=\"+t+=+224%2Fs+\"   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=+224+=+s%2A%28224%2Fs%29+-+8%2A%28224%2Fs%29+%2B+.5s+-+4+ ALIGN=MIDDLE  ALT=\"+224+=+s%2A%28224%2Fs%29+-+8%2A%28224%2Fs%29+%2B+.5s+-+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=+224+=+224+-+8%2A%28224%2Fs%29+%2B+.5s+-+4+ ALIGN=MIDDLE  ALT=\"+224+=+224+-+8%2A%28224%2Fs%29+%2B+.5s+-+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=+4+=++-+8%2A%28224%2Fs%29+%2B+.5s+ ALIGN=MIDDLE  ALT=\"+4+=++-+8%2A%28224%2Fs%29+%2B+.5s+\"   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=+2s+ ALIGN=MIDDLE  ALT=\"+2s+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8s+=+-16%2A224+%2B+s%5E2+ ALIGN=MIDDLE  ALT=\"+8s+=+-16%2A224+%2B+s%5E2+\"   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%5E2+-+8s+-+3584+=+0+ ALIGN=MIDDLE  ALT=\"+s%5E2+-+8s+-+3584+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll complete the square<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%5E2+-+8s+=+3584++ ALIGN=MIDDLE  ALT=\"+s%5E2+-+8s+=+3584++\"   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%5E2+-+8s+%2B+%28-8%2F2%29%5E2+=+3584+%2B+%28-8%2F2%29%5E2++ ALIGN=MIDDLE  ALT=\"+s%5E2+-+8s+%2B+%28-8%2F2%29%5E2+=+3584+%2B+%28-8%2F2%29%5E2++\"   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%5E2+-+8s+%2B+16+=+3584+%2B+16++ ALIGN=MIDDLE  ALT=\"+s%5E2+-+8s+%2B+16+=+3584+%2B+16++\"   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+s+-+4+%29%5E2+=+3600+ ALIGN=MIDDLE  ALT=\"+%28+s+-+4+%29%5E2+=+3600+\"   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+s+-+4+%29%5E2+=+60%5E2+ ALIGN=MIDDLE  ALT=\"+%28+s+-+4+%29%5E2+=+60%5E2+\"   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+-+4+=+60+ ALIGN=MIDDLE  ALT=\"+s+-+4+=+60+\"   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+=+64+ ALIGN=MIDDLE  ALT=\"+s+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ( ignore the negative square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+-+8+=+56+ ALIGN=MIDDLE  ALT=\"+s+-+8+=+56+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The train's speed on the way back is 56 km/hr<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+224+=+56%2A%28+t+%2B+.5+%29+ ALIGN=MIDDLE  ALT=\"+224+=+56%2A%28+t+%2B+.5+%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=+t+%2B+.5+=+224%2F56+ ALIGN=MIDDLE  ALT=\"+t+%2B+.5+=+224%2F56+\"   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+%2B+.5+=+4+ ALIGN=MIDDLE  ALT=\"+t+%2B+.5+=+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=+t+=+3.5+ ALIGN=MIDDLE  ALT=\"+t+=+3.5+\"   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=+224+=+s%2At+ ALIGN=MIDDLE  ALT=\"+224+=+s%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=+224+=+64t+ ALIGN=MIDDLE  ALT=\"+224+=+64t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+224%2F64+ ALIGN=MIDDLE  ALT=\"+t+=+224%2F64+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+3.5+ ALIGN=MIDDLE  ALT=\"+t+=+3.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );