document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189622>Question 1189622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A girl starts a hike up the mountain at 6 am. 2 hours into the hike she is passed up by a group of people on their way up. At 10 am, the same group of people passes her again on the way down. She finally reached the summit at noon. If the girl and the group of people traveled at constant speeds, at what time did the group reach the summit?\r<BR>\n" );
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document.write( "sorry I asked this question yesterday but missed an important part (that she reached the summit at noon). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821048 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821048\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Draw out a number line with these important points<ul><li>A = the girl's location at 8 AM (the other hikers are here as well; both groups start to travel the same direction)</li><li>B = the girl's location at 10 AM (the hikers are passing the girl in the opposite direction)</li><li>C = the mountain top's location</li></ul>We don't need to plot the 6 AM location because everything effectively starts at 8 AM.\r<BR>\n" );
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document.write( "The girl travels from A to B in 2 hours  (8 AM to 10 AM)<BR>\n" );
document.write( "The girl travels from B to C in 2 hours (10 AM to 12 PM)<BR>\n" );
document.write( "Since she's traveling at the same rate and each segment is the same time duration, this means segments AB and BC are the same length, which I'll call x.\r<BR>\n" );
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document.write( "The hiking group travels AB, BC and BC again before meeting up with the girl a second time.<BR>\n" );
document.write( "They travel AB+BC+BC = x+x+x = 3x distance units in the same time the girl travels AB = x distance units. \r<BR>\n" );
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document.write( "The jump from x to 3x tells us that the hiking group is 3 times faster than the girl.\r<BR>\n" );
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document.write( "This must mean that the hiking group takes 1/3 as much time to reach the summit compared to the girl.\r<BR>\n" );
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document.write( "It takes the girl 4 hours to reach the summit (from 8 AM to 12 PM) when starting at point A<BR>\n" );
document.write( "We take 1/3 of this to get the hiking group's duration<BR>\n" );
document.write( "(1/3)*(4 hours) = (1/3)*(240 minutes) = 80 minutes<BR>\n" );
document.write( "80 min = 60 min + 20 min = 1 hour + 20 min\r<BR>\n" );
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document.write( "The hiking group starts at 8 AM and take 80 minutes (aka 1 hour, 20 min) to reach the top\r<BR>\n" );
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document.write( "8:00 AM + (1 hour, 20 min) = <font color=red>9:20 AM</font> is the final answer. <BR>\n" );
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