An airplane at an altitude of 35,000 feet begins descending at a rate of 2,000 feet per minute. 



a) Write an equation to model this problem.

y =  
 



b) How long will it take the airplane to reach the ground?

 
 minutes

Let's break this problem into parts.

### a) Writing the equation:

The airplane is at an initial altitude of 35,000 feet, and it is descending at a rate of 2,000 feet per minute. Let:

- \( y \) represent the altitude (in feet) after \( t \) minutes.
- \( t \) represent the time in minutes.

Since the airplane is descending, the altitude decreases by 2,000 feet every minute. The equation to model this situation is:

\[
y = 35,000 - 2,000t
\]

where:
- \( y \) is the altitude after \( t \) minutes,
- \( 35,000 \) is the initial altitude,
- \( 2,000t \) is the total altitude lost after \( t \) minutes.

---

### b) How long will it take the airplane to reach the ground?

To find when the airplane reaches the ground, set \( y = 0 \) (since the altitude is 0 when the airplane is on the ground), and solve for \( t \):

\[
0 = 35,000 - 2,000t
\]

Now, solve for \( t \):

\[
2,000t = 35,000
\]

\[
t = \frac{35,000}{2,000} = 17.5 \text{ minutes}
\]

So, it will take **17.5 minutes** for the airplane to reach the ground.

---

Do you have any questions or would you like more details?

Here are 5 related questions to consider:
1. What would happen if the descent rate was faster, say 3,000 feet per minute?
2. How would you modify the equation if the airplane started descending from 40,000 feet instead of 35,000 feet?
3. What if the airplane descended at a non-constant rate, how would you model that?
4. How much altitude would the airplane have lost after 10 minutes?
5. How would you calculate the altitude after descending for half the time it takes to reach the ground?

### Tip:
When solving linear equations, always identify the rate of change and the starting value to set up your equation efficiently.

An airplane at an altitude of 35,000 feet begins descending at a rate of 2,000 feet per minute. a) Write an equation to model this problem. b) How long will it take the airplane to reach the ground?

Learn how to model the descent of an airplane using linear equations. This problem involves calculating how long it takes for an airplane descending at 2,000 feet per minute to reach the ground from an altitude of 35,000 feet. Suitable for students in Grades 6-8.

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