Question

lane at an altitude of 35,000 feet begins descending at a rate of 2,000 feet per minute. and solve a linear equation to find how long it will take the airplane to reach the ground?

Explanation:

Step1: Define the linear equation

Let \( y \) be the altitude of the airplane (in feet) and \( x \) be the time (in minutes). The initial altitude is 35,000 feet, and it descends at 2,000 feet per minute. So the equation is \( y = -2000x + 35000 \). We want to find when \( y = 0 \) (reaches the ground).

Step2: Solve for \( x \) when \( y = 0 \)

Set \( y = 0 \) in the equation:
\( 0 = -2000x + 35000 \)

Step3: Isolate \( x \)

Add \( 2000x \) to both sides:
\( 2000x = 35000 \)

Step4: Divide to find \( x \)

Divide both sides by 2000:
\( x = \frac{35000}{2000} = 17.5 \)

Answer:

17.5 minutes