Question

a submarine is cruising at 925 feet below sea level. it then rises in two stages, as shown, and finally reaches a depth of 200 feet below sea level.

. in stage 1, the submarine rises 20% of its initial distance below sea level
. in stage 2, the submarine rises at a rate of 13.5 feet per minute.
how long did the submarine rise during stage 2, in minutes

Answer 1

To determine how long the submarine rose during stage 2 in minutes, we need to follow these steps:

1. **Calculate the initial depth of the submarine:**
The submarine is initially at 925 feet below sea level.

2. **Calculate the rise in stage 1:**
In stage 1, the submarine rises 20% of its initial depth.
\[
\text{Rise in stage 1} = 0.20 \times 925 = 185 \text{ feet}
\]

3. **Calculate the new depth after stage 1:**
After rising 185 feet, the new depth is:
\[
925 - 185 = 740 \text{ feet below sea level}
\]

4. **Determine the final depth:**
The submarine's final depth is 200 feet below sea level.

5. **Calculate the total rise needed to reach the final depth:**
The total rise required from the depth after stage 1 to the final depth is:
\[
\text{Rise needed} = 740 - 200 = 540 \text{ feet}
\]

6. **Calculate the time taken in stage 2:**
In stage 2, the submarine rises at a rate of 13.5 feet per minute. Thus, the time taken for stage 2 is:
\[
\text{Time} = \frac{\text{Rise needed}}{\text{Rate}} = \frac{540}{13.5}
\]

Performing the calculation:
\[
\text{Time} = \frac{540}{13.5} = 40 \text{ minutes}
\]

So, the submarine rose for **40 minutes** during stage 2.