To find the change in altitude during the descent, we need to calculate the difference between the starting altitude and the ending altitude.
Let:
- \( h_{\text{start}} \) = the starting altitude (1.55 miles)
- \( h_{\text{end}} \) = the ending altitude (0.75 miles)
We can express the change in altitude (\( \Delta h \)) with the following equation:
\[ \Delta h = h_{\text{start}} - h_{\text{end}} \]
Substituting the values:
\[ \Delta h = 1.55 , \text{miles} - 0.75 , \text{miles} \]
Calculating the difference:
\[ \Delta h = 1.55 - 0.75 = 0.80 , \text{miles} \]
Thus, the change in altitude is \( 0.80 \) miles.
Explanation of the Answer:
The hiker descended a total of 0.80 miles over the course of 4 hours, which means that they went from a higher altitude of 1.55 miles to a lower altitude of 0.75 miles. This indicates a significant drop in altitude as the hiker moves down the mountain.