As an airplane rises, the outside temperature drops 3.6°F for each 1000 feet of elevation gain. Suppose the outside temperature is 65°F on the ground when the plane takes off and -43°F at cruising altitude. How high is the plane then? Algebra

Question

As an airplane rises, the outside temperature drops 3.6°F for each 1000 feet of elevation gain. Suppose the outside temperature is 65°F on the ground when the plane takes off and -43°F at cruising altitude. How high is the plane then? Algebra

Answer 1

Let x be the altitude gain in thousands of feet. The temperature change is then -3.6x°F. The temperature at cruising altitude is -43°F. Setting up the equation, we get:

65 - 3.6x = -43

Adding 3.6x to both sides:

65 = -43 + 3.6x

Adding 43 to both sides:

108 = 3.6x

Dividing both sides by 3.6:

x = 30

Therefore, the plane is at an altitude of 30,000 feet.