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.