Question

an airplane at an altitude of 35,000 feet begins descending at a rate of 2,000 feet per minu write and solve a linear equation to find how long it will take the airplane to reach the gro linear equation: lution:

Explanation:

Step1: Define variables and equation

Let \( t \) be the time in minutes and \( h \) be the altitude in feet. The initial altitude is 35,000 feet, and it descends at 2,000 feet per minute. When it reaches the ground, \( h = 0 \). The linear equation is \( h = 35000 - 2000t \). To find when \( h = 0 \), set up \( 0 = 35000 - 2000t \).

Step2: Solve for \( t \)

Add \( 2000t \) to both sides: \( 2000t = 35000 \). Then divide both sides by 2000: \( t=\frac{35000}{2000}=17.5 \).

Answer:

The linear equation is \( h = 35000 - 2000t \) (or \( 0 = 35000 - 2000t \) when solving for ground level), and the time to reach the ground is \( 17.5 \) minutes.