document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=638020>Question 638020</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At the same time, two hikers took off, one from city B to city A and the other from city A to city B. They hiked the same distance and their speeds were constant. They met on the way, and it was revealed that the hiker from city B to city A traveled two km more than the other hiker. This hiker arrived to city A 40 minutes after the two met, and the hiker from city A arrived to city B an hour and a half after they met. What is the distance of the trail? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #402254 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=402254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At the same time, two hikers took off, one from city B to city A and the other<BR>\n" );
document.write( " from city A to city B.<BR>\n" );
document.write( "They hiked the same distance and their speeds were constant.<BR>\n" );
document.write( "They met on the way, and it was revealed that the hiker from city B to city A<BR>\n" );
document.write( " traveled two km more than the other hiker. <BR>\n" );
document.write( "This hiker arrived to city A 40 minutes after the two met, and the hiker from<BR>\n" );
document.write( " city A arrived to city B an hour and a half after they met.<BR>\n" );
document.write( " What is the distance<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Do this using minutes for the time<BR>\n" );
document.write( "let t = travel time to the point where they met<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let x = dist from A to the meeting point<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(x+2) = dist from B to the meeting point<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x + (x+2) = 2x+2 km is the distance from A to B<BR>\n" );
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document.write( "A<-----40min------*---------t min-------< B(hiker B's path)\r<BR>\n" );
document.write( "\n" );
document.write( "A------x km-------*-------(x+2)km-------B\r<BR>\n" );
document.write( "\n" );
document.write( "A>-----t Min------*--------90min--------> B (hiker A's path)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Hiker B,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F40 ALIGN=MIDDLE  ALT=\"t%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B2%29%29%2Fx ALIGN=MIDDLE  ALT=\"%28%28x%2B2%29%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "tx = 40(x+2)<BR>\n" );
document.write( "tx = 40x + 80<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2840x%2B80%29%2Fx ALIGN=MIDDLE  ALT=\"%2840x%2B80%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Hiker A<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F90 ALIGN=MIDDLE  ALT=\"t%2F90\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "t(x+2) = 90x<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2890x%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%2890x%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "t=t, therefore:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2890x%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%2890x%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2840x%2B80%29%2Fx ALIGN=MIDDLE  ALT=\"%2840x%2B80%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "90x^2 = (x+2)(40x+80)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "90x^2 = 40x^2 + 80x + 80x + 160<BR>\n" );
document.write( "90x^2 = 40x^2 + 160x + 160<BR>\n" );
document.write( "Combine on the left<BR>\n" );
document.write( "90x^2 - 40x^2 - 160x - 160 = 0<BR>\n" );
document.write( "50x^2 - 160x - 160 = 0<BR>\n" );
document.write( "Simplify, divide by 10<BR>\n" );
document.write( "5x^2 - 16x - 16 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(5x + 4)(x - 4) = <BR>\n" );
document.write( "The positive solution is all we want here<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "\"What is the distance?\"<BR>\n" );
document.write( "2(4) + 2 = 10 km is the distance from A to B<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Confirm this, find t<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2890%2A4%29%2F%284%2B2%29 ALIGN=MIDDLE  ALT=\"%2890%2A4%29%2F%284%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 60 min<BR>\n" );
document.write( "Find the speed of A & B<BR>\n" );
document.write( "A's time in hrs (90+60)/60 = 2.5 hrs<BR>\n" );
document.write( "A's speed 10/2.5 = 4 km/hr<BR>\n" );
document.write( "and<BR>\n" );
document.write( "B's time in hrs (40+60)/60 = 1<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "A's speed 10/1.67 ~ 6 km/hr<BR>\n" );
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document.write( "Find how far each traveled in 1 hr (t)<BR>\n" );
document.write( "B: 6 km <BR>\n" );
document.write( "A: 4 km<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "dif: 2 km<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );