Laura's Final Position Calculation on Mt. Hood

Laura's Final Position on Mt. Hood

Laura is 2 kilometers below her campsite on Mt. Hood. She hikes down 3 1/6 kilometers to the Hood River and then hikes up 4 3/4 kilometers back up the mountain. What is Laura's final position relative to her campsite?

Final answer:

Laura's final position relative to her campsite is -5/12 kilometers, indicating she is slightly below the starting point.

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:


  • Initial Position: -2 km (below campsite)

  • Hike Down: -19/6 km (further below)

  • 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.

What is Laura's final position relative to her campsite on Mt. Hood after hiking down and then back up the mountain? Laura's final position relative to her campsite is -5/12 kilometers, indicating she is slightly below her starting point on Mt. Hood.
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