Jamison decided to go for a hike one day. He started early before the sun came up, following a trail to a central hill. As he arrived at the hill, the sun was just starting to rise, and Jamison’s shadow started forming on the ground. At this point, he started walking 3 miles with his shadow on his left, then turned to walk 2.5 miles with his shadow behind him. After this, Jamison turned to walk 1.5 miles with his shadow to his right, and finally turned to walk 4 miles with his shadow behind him again. At this point, Jamison became tired and took a nap. When he woke up, he decided he would walk back the same way he came. This means, for example, if he walked for 1 mile with his shadow behind him, then going back he would walk 1 mile with his shadow in front of him. There was one issue with this: when Jamison woke up from his nap, it was after 2:00p.m. He didn’t realize that his shadows changed direction. After he completes his “backward directions”, where is Jamison relative to the hill in which he started these directions? (Acceptable answers look like x miles north and y miles west)
Assuming shadows are straight east/west/north/south, he:
1) walked 3 miles shadow on left, so headed north 3 miles
2) 2.5 miles with shadow behind him, so east 2.5 miles
3) 1.5 miles with shadow to right, so 1.5 miles south,
4) 4 miles with shadow behind him, so 4. miles east
Now afternoon, so things change a little.
5) 4 miles with shadow in front of him, so 4 miles east
6) 1.5 miles with shadow to left, so 1.5 miles south
7) 2.5 miles with shadow in front of him, so 2.5 miles east
8) 3 miles with shadow on right, so 3 miles north.
Add/subtract north and south as well as east and west
3 north - 1.5 south - 1.5 south + 3 north = 3 north
2.5 east + 4 east + 4 east + 2.5 east = 13 east
Jamison is lost, should rely on cell phone GPS tracking instead of the sun.
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