Two hikers, Manny and Alicia begin their climb at 8 am up Mount Hunt. They eat breakfast at the 500-foot rest stop and enjoy the view for half an hour
beginning at 9 am. They continue up the trail, and their pace has increased because
they have now had breakfast and are fully awake. At 10:15 am they stop for a 15-
minute break at the 1000-foot rest stop and then continue up the trail. This time
their pace has slowed since they've been hiking for close to two hours. At noon
they reach the 1500-foot level and stop for an hour lunch break. It has become hot
and humid, and their pace the remainder of the afternoon is pretty lethargic. At 5
pm, they finally reach the summit at 2800-feet. They set-up their campsite, make
supper, and enjoy the wonderful view.
The next moming they pack everything and begin back down the mountain
on a different trail at 8 am, the same time they started yesterday. It is a bright and
sunny day, and they enjoy the beautiful view as they descend down the mountain at
a steady rate until they reach the bottom. They arrive at the base of Mount Hunt at
the same time that they arrived at the summit the day before.
Now the heated discussion begins. Alicia feels that at some time during the
two days they must have been at the same height at exactly the same time of day.
Manny is adamant with the opposite opinion, they were never at the same height at
the same time during the two days.
Who is correct? Defend your choice in as many different ways that you can.
Can this situation be modeled using equations? If so, write the equations. If not,
explain