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The problem presents two drones descending at different rates and asks us to find how many minutes it will take for the black drone to descend to be at the same altitude as or lower than the white drone. 

We are asked to choose what the variable \( n \) represents, and based on the context, the most appropriate choice would be:

- **Let \( n \) represent the number of minutes.**

### To set up the equation or inequality:

- The black drone starts at an altitude of **1,170 feet** and descends at **64 feet per minute**.
- The white drone starts at an altitude of **966 feet** and descends at **52 feet per minute**.

We need to find when the black drone’s altitude is equal to or less than the white drone's altitude.

#### Step 1: Set up the expression for each drone's altitude after \( n \) minutes:
- Altitude of the black drone after \( n \) minutes:  
  \[
  1170 - 64n
  \]
- Altitude of the white drone after \( n \) minutes:  
  \[
  966 - 52n
  \]

#### Step 2: Set up the inequality to find when the black drone is at most the same altitude as the white drone:
\[
1170 - 64n \leq 966 - 52n
\]

#### Step 3: Solve the inequality:
\[
1170 - 64n \leq 966 - 52n
\]
Subtract 966 from both sides:
\[
204 - 64n \leq -52n
\]
Add \( 64n \) to both sides:
\[
204 \leq 12n
\]
Divide by 12:
\[
n \geq \frac{204}{12} = 17
\]

So, it will take **at least 17 minutes** for the black drone to reach the same altitude as the white drone.

---

Would you like more details on the steps? Here are five related questions to explore further:

1. What happens if the drones start at the same altitude but with different descent rates?
2. How would the equation change if the white drone descends faster than the black drone?
3. How would you set up the problem if both drones were rising instead of descending?
4. Can you write a general equation for similar drone problems with different starting altitudes and rates of descent?
5. What if a third drone is introduced with a different altitude and rate?

**Tip:** When working with inequalities, always carefully check which variable represents the greater rate to set up the correct relationship between the two quantities.

Two drones are descending from the sky in vertical lines. A black drone is currently at an altitude of 1,170 feet and is dropping at a rate of 64 feet per minute. A white drone is at an altitude of 966 feet and is dropping at a rate of 52 feet per minute. How many minutes will it take for the black drone to be at most the same altitude as the white drone? Use the variable n to represent the unknown quantity.

Learn how to solve a problem involving two drones descending at different rates. This problem demonstrates how to set up and solve an inequality to determine when one drone reaches the same altitude as another. Key algebraic concepts include solving linear inequalities and calculating rates of change. Suitable for students in Grades 8-10.

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