document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980173>Question 980173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There was a question about an army travelling 5 mph and a messenger on horseback travelling  at 10 mph(question asks for the distance from front to rear) that was answered by ankor@dixie.net that I didn't really understand why did he add and subtract 5 to the 10 mph rate. I know that you do add +-r or a given amount in wind and water current problems. Is that why you added and subtracted the 5? Some logic of why is all I need, so that I can understand a problem that I've never seen before in any other place than the Schaum College Algebra textbook. Please help. QUESTION: WHY WAS THE 5 ADDED AND SUBTRACTED FROM 10 TO GET 15 AND 5(Denominators) AND WHY 5 AND NOT R? Anybody that understands fully why and can explain is welcome. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601381 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Let &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; be the length of army's column &nbsp;(line)&nbsp; in miles.\r<BR>\n" );
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document.write( "When the messenger is moving from the front to the rear, &nbsp;he moves in the direction opposite the the army's move. &nbsp;Therefore, &nbsp;his speed relative to the army's column is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2B5 ALIGN=MIDDLE  ALT=\"10%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mi%2Fh ALIGN=MIDDLE  ALT=\"mi%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;and he spends &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F15 ALIGN=MIDDLE  ALT=\"d%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; hours to get from the front to the rear.\r<BR>\n" );
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document.write( "On the way back the messenger moves in the same direction as the army's column moves. &nbsp;Therefore, &nbsp;his speed relative to the army's column is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-5 ALIGN=MIDDLE  ALT=\"10-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mi%2Fh ALIGN=MIDDLE  ALT=\"mi%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;and he spends &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F5 ALIGN=MIDDLE  ALT=\"d%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours to get from the rear to the front.\r<BR>\n" );
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document.write( "Therefore, &nbsp;the equation is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F15 ALIGN=MIDDLE  ALT=\"d%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F5 ALIGN=MIDDLE  ALT=\"d%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  &nbsp;&nbsp;&nbsp;&nbsp;(10 minutes = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > of hour).\r<BR>\n" );
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document.write( "Solve it by simplifying step by step:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F15 ALIGN=MIDDLE  ALT=\"d%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3d%2F15 ALIGN=MIDDLE  ALT=\"3d%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "d + 3d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F6 ALIGN=MIDDLE  ALT=\"15%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "4d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F6 ALIGN=MIDDLE  ALT=\"15%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F24 ALIGN=MIDDLE  ALT=\"15%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles.\r<BR>\n" );
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document.write( "<B>Answer</B>.  &nbsp;The distance from the front to the rear is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F24 ALIGN=MIDDLE  ALT=\"15%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; miles.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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