A student is planning to hike a mountain that has three peaks. The third peak is the highest peak on the mountain and its height is 2,304 feet above sea level.

Question

In order to reach the third peak the student must pass through the first peak followed by the second peak. The height of the first peak is 1,152 feet above sea level and the height of the second peak is 800 feet below the third peak.

What is the difference, in feet, between the height of the second peak and the height of the first peak?

​
feet

Answer 1

To find the height of the second peak, we can start with the height of the third peak, which is 2,304 feet. Since the second peak is 800 feet below the height of the third peak, we can calculate the height of the second peak as follows:

\[ \text{Height of second peak} = \text{Height of third peak} - 800 \text{ feet} \] \[ \text{Height of second peak} = 2,304 \text{ feet} - 800 \text{ feet} = 1,504 \text{ feet} \]

Now, we have the heights of both peaks:

• Height of the first peak: 1,152 feet
• Height of the second peak: 1,504 feet

Next, we find the difference in height between the second peak and the first peak:

\[ \text{Difference} = \text{Height of second peak} - \text{Height of first peak} \] \[ \text{Difference} = 1,504 \text{ feet} - 1,152 \text{ feet} = 352 \text{ feet} \]

Therefore, the difference in height between the second peak and the first peak is:

\[ \boxed{352} \text{ feet} \]