document.write( "Question 1189622: 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
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Algebra.Com's Answer #821351 by MathTherapy(10552) $\"\"$ $\"About$

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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
\n" ); document.write( "\n" ); document.write( "sorry I asked this question yesterday but missed an important part (that she reached the summit at noon).
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Let distance the girl travelled up the mountain be D\r\n" );
document.write( "Since it took her 6 hours (6:00 a.m. - 12:00 noon) to get to summit, her speed = \r\n" );
document.write( "When the group passed her at 8:00 a.m. - 2 hours after her departure - she had travelled a distance of  \r\n" );
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document.write( "At 10:00 a.m., or 4 hours into the trip, she’d travelled a distance of \r\n" );
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document.write( "When she’d travelled a distance of  for 4 hours (6:00 a.m. to 10:00 a.m.), the group had travelled a distance\r\n" );
document.write( "of  in 2 hours (between meetings, up and down). Therefore, group’s speed  = \r\n" );
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document.write( "They 1^st met at the  mark, so at that time, the group had to travel  to get to the summit\r\n" );
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document.write( "With the group’s speed being , and as it (the group) travelled a distance of , after meeting her the 1^st time, the\r\n" );
document.write( "group took  to get to the summit.\r\n" );
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document.write( "Since the group met her 1^st, at 8:00 a.m., and took  hours (1 hour, 20 minutes), thereafter, to get to summit, the group reached \r\n" );
document.write( "the summit 1 hour and 20 minutes after 8:00 a.m., which is \r\n" );
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document.write( "If this is too complex to follow, then just substitute actual numbers, and it should be quite easy to understand.

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