document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=879989>Question 879989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two brothers start at same time from two places 20 kms apart. If they walk in same<BR>\n" );
document.write( "direction, elder brother overtakes the younger in 10 hrs, but if they walk in opposite<BR>\n" );
document.write( "directions, they meet in 2 hrs. Find the rates at which they walk. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #531184 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=531184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the rate of the elder brother = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let the rate of the younger brother = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B2%5D+ ALIGN=MIDDLE  ALT=\"+r%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "The elder brother has to have the faster rate<BR>\n" );
document.write( "in order to catch up with the younger brother<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "Also, when they walk in opposite directions,<BR>\n" );
document.write( "they must be walking towards each other, or<BR>\n" );
document.write( "else they would never meet<BR>\n" );
document.write( "----------------------------<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;\" > = distance the elder brother has<BR>\n" );
document.write( "to travel to catch younger brother<BR>\n" );
document.write( "Walking in same direction:<BR>\n" );
document.write( "Equation for younger brother:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+-+20+=+r%5B2%5D%2A10+ ALIGN=MIDDLE  ALT=\"+d+-+20+=+r%5B2%5D%2A10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation for elder brother:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+r%5B1%5D%2A10+ ALIGN=MIDDLE  ALT=\"+d+=+r%5B1%5D%2A10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Walking towards each other:<BR>\n" );
document.write( "Think of this as the elder brother moving<BR>\n" );
document.write( "at the sum of their speeds and the <BR>\n" );
document.write( "younger brother not moving<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+=+%28+r%5B1%5D+%2B+r%5B2%5D+%29%2A2+ ALIGN=MIDDLE  ALT=\"+20+=+%28+r%5B1%5D+%2B+r%5B2%5D+%29%2A2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<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=+10r%5B1%5D+-+20+=+10r%5B2%5D+ ALIGN=MIDDLE  ALT=\"+10r%5B1%5D+-+20+=+10r%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2A%28+r%5B1%5D+-+r%5B2%5D+%29+=+20+ ALIGN=MIDDLE  ALT=\"+10%2A%28+r%5B1%5D+-+r%5B2%5D+%29+=+20+\"   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%5B1%5D+-+r%5B2%5D+=+2+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+-+r%5B2%5D+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+%2B+r%5B2%5D+=+10+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+%2B+r%5B2%5D+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Add (1) and (3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2r%5B1%5D+=+12+ ALIGN=MIDDLE  ALT=\"+2r%5B1%5D+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+=+6+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+%2B+r%5B2%5D+=+10+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+%2B+r%5B2%5D+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+%2B+r%5B2%5D+=+10+ ALIGN=MIDDLE  ALT=\"+6+%2B+r%5B2%5D+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B2%5D+=+4+ ALIGN=MIDDLE  ALT=\"+r%5B2%5D+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The eldest brother's rate is 6 km/hr<BR>\n" );
document.write( "The younger brother's rate is 4 km/hr<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+r%5B1%5D%2A10+ ALIGN=MIDDLE  ALT=\"+d+=+r%5B1%5D%2A10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <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;\" > km<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+-+20+=+r%5B2%5D%2A10+ ALIGN=MIDDLE  ALT=\"+d+-+20+=+r%5B2%5D%2A10+\"   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+=+4%2A10+%2B+20+ ALIGN=MIDDLE  ALT=\"+d+=+4%2A10+%2B+20+\"   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;\" > km<BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );