https://file.aiquickdraw.com/mathbot/file/1730514529883n6ucxz8r.jpg

To solve this problem, let's go through the steps for each part:

### Part (a): Finding the Vertical Distance Traveled

1. **Identify Initial and Final Depths**:
   - The submarine was initially at \(-725.6\) feet (3 hours ago).
   - Its current depth is \(-314.9\) feet.

2. **Calculate the Vertical Distance**:
   - To find the vertical distance, calculate the difference between the initial and final depths.
   - \[
   \text{Vertical Distance} = -314.9 - (-725.6)
   \]
   - Simplify this by adding the opposite:
   - \[
   \text{Vertical Distance} = -314.9 + 725.6 = 410.7 \text{ feet}
   \]

   So, the answer for part (a) is:
   \[
   \text{Vertical Distance} = 410.7 \text{ feet}
   \]

### Part (b): Finding the Mean Hourly Vertical Distance

1. **Calculate the Time**:
   - The submarine traveled this distance over a period of 3 hours.

2. **Calculate the Mean Hourly Distance**:
   - Divide the total vertical distance by the time to find the rate of change per hour.
   - \[
   \text{Mean Hourly Distance} = \frac{410.7}{3} \approx 136.9 \text{ feet per hour}
   \]

   So, the answer for part (b) is:
   \[
   \text{Mean Hourly Distance} \approx 136.9 \text{ feet per hour}
   \]

### Summary
- **(a)** The vertical distance traveled is **410.7 feet**.
- **(b)** The mean hourly vertical distance traveled is approximately **136.9 feet per hour**.

Would you like further details on any of these calculations? 

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Here are 5 related questions for further practice:

1. If the submarine started at a depth of -800 feet and rose to -200 feet in 4 hours, what is the total vertical distance traveled?
2. How would the mean hourly distance change if the submarine took 6 hours to travel the same vertical distance?
3. If the submarine traveled a vertical distance of 500 feet in 5 hours, what is its mean hourly vertical distance?
4. How would you calculate the vertical distance if the submarine moved downwards instead of upwards?
5. If the submarine started at -314.9 feet and moved down to -800 feet, what would be the new vertical distance?

**Tip**: When calculating differences involving negative values, always remember to add the opposite value to simplify the calculation.

The figure shows the depths of a submarine. 
a) Find the vertical distance traveled by the submarine. Write your answer as a decimal.
b) Find the mean hourly vertical distance traveled by the submarine. Write your answer as a decimal.

Learn how to calculate the vertical distance traveled by a submarine from -725.6 feet to -314.9 feet over 3 hours. This problem covers distance calculation and mean rate calculation, suitable for students in Grades 6-8.

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