document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=824121>Question 824121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man cycled a distance of 42km from his village. On his return journey he increased his speed by 2km/hr and took half an hour less. Calculate the average speed on the journey from his village. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #496113 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=496113\">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=+r+ ALIGN=MIDDLE  ALT=\"+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = his rate going from the village in km/hr<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;\" > = his time in hrs going from the village<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Equation going from the village:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+42+=+r%2At+ ALIGN=MIDDLE  ALT=\"+42+=+r%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation for return journey:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+42+=+%28+r%2B2+%29%2A%28+t+-+.5+%29+ ALIGN=MIDDLE  ALT=\"+42+=+%28+r%2B2+%29%2A%28+t+-+.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=+42+=+r%2At+%2B+2t+-+.5r+-+1+ ALIGN=MIDDLE  ALT=\"+42+=+r%2At+%2B+2t+-+.5r+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+43+%2B+.5r+=+r%2At+%2B+2t+ ALIGN=MIDDLE  ALT=\"+43+%2B+.5r+=+r%2At+%2B+2t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+43+%2B+.5r+=+%28+r+%2B+2+%29%2At+ ALIGN=MIDDLE  ALT=\"+43+%2B+.5r+=+%28+r+%2B+2+%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=+t+=+%28+43+%2B+.5r+%29+%2F+%28+r+%2B+2+%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+43+%2B+.5r+%29+%2F+%28+r+%2B+2+%29+\"   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=+42%2Fr+=+t+ ALIGN=MIDDLE  ALT=\"+42%2Fr+=+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+42%2Fr+=+%28+43+%2B+.5r+%29+%2F+%28+r+%2B+2+%29+ ALIGN=MIDDLE  ALT=\"+42%2Fr+=+%28+43+%2B+.5r+%29+%2F+%28+r+%2B+2+%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=+r%2A%28+r+%2B+2+%29+ ALIGN=MIDDLE  ALT=\"+r%2A%28+r+%2B+2+%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=+42%2A%28+r%2B2+%29+=+%28+43+%2B+.5r+%29%2Ar+ ALIGN=MIDDLE  ALT=\"+42%2A%28+r%2B2+%29+=+%28+43+%2B+.5r+%29%2Ar+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+42r+%2B+84+=+43r+%2B+.5r%5E2+ ALIGN=MIDDLE  ALT=\"+42r+%2B+84+=+43r+%2B+.5r%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.5r%5E2+%2B+r+-+84+=+0+ ALIGN=MIDDLE  ALT=\"+.5r%5E2+%2B+r+-+84+=+0+\"   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%5E2+%2B+2r+-+168+=+0+ ALIGN=MIDDLE  ALT=\"+r%5E2+%2B+2r+-+168+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+r+=+%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+=+1+ ALIGN=MIDDLE  ALT=\"+a+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+2+ ALIGN=MIDDLE  ALT=\"+b+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-42+ ALIGN=MIDDLE  ALT=\"+c+=+-42+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+%28-2+%2B-+sqrt%28+2%5E2+-+4%2A1%2A%28-168%29+%29%29+%2F+%282%2A1%29+ ALIGN=MIDDLE  ALT=\"+r+=+%28-2+%2B-+sqrt%28+2%5E2+-+4%2A1%2A%28-168%29+%29%29+%2F+%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+%28-2+%2B-+sqrt%28+4+%2B+672+%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+r+=+%28-2+%2B-+sqrt%28+4+%2B+672+%29%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+%28-2+%2B-+sqrt%28+676+%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+r+=+%28-2+%2B-+sqrt%28+676+%29%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+%28-2+%2B+26%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+r+=+%28-2+%2B+26%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=++-1+%2B+13%0D%0A%7B%7B%7B+r+=+12+ ALIGN=MIDDLE  ALT=\"+r+=++-1+%2B+13%0D%0A%7B%7B%7B+r+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "His average rate traveling from the village was 12 km/hr<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+42+=+r%2At+ ALIGN=MIDDLE  ALT=\"+42+=+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=+t+=+42%2F12+ ALIGN=MIDDLE  ALT=\"+t+=+42%2F12+\"   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( "-----------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+42+=+%28+r%2B2+%29%2A%28+t+-+.5+%29+ ALIGN=MIDDLE  ALT=\"+42+=+%28+r%2B2+%29%2A%28+t+-+.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=+42+=+%28+12+%2B+2+%29%2A%28+3.5+-+.5+%29+ ALIGN=MIDDLE  ALT=\"+42+=+%28+12+%2B+2+%29%2A%28+3.5+-+.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=+42+=+14%2A3+ ALIGN=MIDDLE  ALT=\"+42+=+14%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=+42+=+42+ ALIGN=MIDDLE  ALT=\"+42+=+42+\"   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" );