At 8 a.m., a hiker begins descending a mountain. The altitude at the starting point is 1.55 miles above sea level. By noon, the hiker has reached an altitude of 0.75 miles above sea level.

Question

What is the change in altitude during these four hours? Write and solve an equation to show your answer. Explain what your answer means.

Answer 1

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.