Currently, your plane is cruising at an altitude of 33,000 feet and holding steady. You are instructed from the airline control tower that you need to get to a crusing altitude either below 31,000 or above 35,000 feet. If your plane can comfortably climb at an average rate of 800 feet per minute and descend at an average rate of 500 feet per minute, what is the range of times (in minutes) it will take your plane to be in the instructed cruising altitude?

The range of time it would take the plane to be in the instructed area is 2.5 minutes to 4 minutes.

Step-by-step explanation:

The given parameters are;

The current altitude of the plane = 33,000 feet

The required altitude of the plane = Below 31,000 or above 35,000 feet

The average climbing speed of the plane = 800 feet per minute

The average descending speed of the plane = 500 feet per minute

The difference in the current and required altitudes are;

For climbing we have  35,000 feet - 33,000 feet = 2,000 feet

For descending we have  33,000 feet - 31,000 feet = 2,000 feet

Speed = Distance/Time

∴ Time = Distance/Speed  

Based on the climbing and descending rate, we have;

The time it would take to climb 2,000 feet is t = 2000 feet/(800 feet/minute) = 2.5 minutes

The time it would take to descend 2,000 feet is t = 2000 feet/(500 feet/minute) = 4 minutes

The range of time it would take the plane to be in the instructed area is therefore;

Time for descending to time for ascending, which is 2.5 minutes to 4 minutes.

The range of time it would take the plane to be in the instructed area = 2.5 minutes to 4 minutes.