Final answer:
Laura's final position relative to her campsite is -5/12 kilometers, indicating she is slightly below the starting point.
Step-by-step explanation:
Laura starts 2 kilometers below her campsite. To determine Laura's final position relative to her campsite, we must consider her additional movements. First, she hikes down 3 1/6 kilometers, which can be converted to a mixed fraction: 3 1/6 = 19/6 kilometers.
She then hikes up 4 3/4 kilometers, which can be converted to 4 3/4 = 19/4 kilometers.
To find her final position, we calculate her total vertical displacement from the campsite:
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- Initial Position: -2 km (below campsite)
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- Hike Down: -19/6 km (further below)
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- Hike Up: +19/4 km (toward campsite)
So, we calculate Laura’s final displacement from the campsite by summing these values:
-2 - 19/6 + 19/4 = (-2 * 12/12) - (19/6 * 2/2) + (19/4 * 3/3) = -24/12 - 38/12 + 57/12 = -5/12 km
Therefore, Laura's final position is -5/12 kilometers relative to her campsite, meaning she is slightly below her campsite.