document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=638031>Question 638031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The distance between city A and B is 28 km. Two hikers left from each city (One from city A to city B and the other from city B to city A) heading towards each other at the same speed. The hiker from city A rested for an hour after having walked 9 km and then continued at a speed greater than 1 km/hour than his previous speed, then rested again 4 km away from city B. There he met the hiker from city B, who walked at a constant speed without resting until the two met. What were the speeds of the two hikers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #402276 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=402276\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The distance between city A and B is 28 km. <BR>\n" );
document.write( "Two hikers left from each city (One from city A to city B and the other from<BR>\n" );
document.write( " city B to city A) heading towards each other at the same speed.<BR>\n" );
document.write( "The hiker from city A rested for an hour after having walked 9 km and then<BR>\n" );
document.write( " continued at a speed greater than 1 km/hour than his previous speed, then<BR>\n" );
document.write( " rested again 4 km away from city B. <BR>\n" );
document.write( "There he met the hiker from city B, who walked at a constant speed without<BR>\n" );
document.write( " resting until the two met.<BR>\n" );
document.write( " What were the speeds of the two hikers?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = speed of the two hikers<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+1) = speed of the A after his 1 hr rest<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the distance hiker A traveled after his rest, to meet B, 4 km from City B<BR>\n" );
document.write( "28-9-4 = 15 km<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Fs ALIGN=MIDDLE  ALT=\"9%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F%28s%2B1%29 ALIGN=MIDDLE  ALT=\"15%2F%28s%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fs ALIGN=MIDDLE  ALT=\"4%2Fs\"   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=9%2Fs ALIGN=MIDDLE  ALT=\"9%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F%28s%2B1%29 ALIGN=MIDDLE  ALT=\"15%2F%28s%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fs ALIGN=MIDDLE  ALT=\"4%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%28s%2B1%29%2B15s%29%2F%28s%28s%2B1%29%29 ALIGN=MIDDLE  ALT=\"%289%28s%2B1%29%2B15s%29%2F%28s%28s%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-s%29%2Fs ALIGN=MIDDLE  ALT=\"%284-s%29%2Fs\"   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=%289s%2B9%2B15s%29%2F%28s%28s%2B1%29%29 ALIGN=MIDDLE  ALT=\"%289s%2B9%2B15s%29%2F%28s%28s%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-s%29%2Fs ALIGN=MIDDLE  ALT=\"%284-s%29%2Fs\"   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=%2824s%2B9%29%2F%28s%28s%2B1%29%29 ALIGN=MIDDLE  ALT=\"%2824s%2B9%29%2F%28s%28s%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-s%29%2Fs ALIGN=MIDDLE  ALT=\"%284-s%29%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by s<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824s%2B9%29%2F%28%28s%2B1%29%29 ALIGN=MIDDLE  ALT=\"%2824s%2B9%29%2F%28%28s%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (4 - s)<BR>\n" );
document.write( "24s + 9 = (s+1)(4-s)<BR>\n" );
document.write( "FOIL the right side<BR>\n" );
document.write( "24s + 9 = 4s - s^2  + 4 - s<BR>\n" );
document.write( "24s + 9 = 3s - s^2 + 4 <BR>\n" );
document.write( "Combine on the left<BR>\n" );
document.write( "s^2 + 24s - 3s + 9 - 4 = 0<BR>\n" );
document.write( "s^2 + 21s + 5 = 0<BR>\n" );
document.write( "Actually this equation has two negative solutions so the given scenario is not possible.<BR>\n" );
document.write( "It seems unreasonable, to find a speed, where A travels 24 km (+ a rest),<BR>\n" );
document.write( "while B travels 4 km<BR>\n" );
document.write( " </SPAN>\n" );
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