Use real-world contexts to interpret quotients of rational numbers.

Question

A pilot is flying an airplane. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excessive turbulence. It takes the pilot 3.5 minutes to make this adjustment. Interpret the quotient to describe the rate of change in the plane’s altitude. Give your answer to the nearest hundredth, and remember the plane is descending.
The quotient that best represents the rate of change in the plane’s altitude is _____ feet/minute.
Answer: -1,142.86

Answer 1

To find the rate of change in the plane's altitude, we need to interpret the quotient of the change in altitude and the time it took for that change.

The pilot descends 4,000 feet over a period of 3.5 minutes. To find the rate of change in altitude, we divide the change in altitude by the time taken:

\[ \text{Rate of change} = \frac{\text{Change in altitude}}{\text{Time}} = \frac{-4000 \text{ feet}}{3.5 \text{ minutes}} \]

Now we perform the division:

\[ \text{Rate of change} = -1142.8571428571428571 \text{ feet/minute} \]

Rounding this to the nearest hundredth gives:

\[ \text{Rate of change} \approx -1142.86 \text{ feet/minute} \]

Since the plane is descending, the rate of change is negative. Thus, the quotient that best represents the rate of change in the plane’s altitude is:

Answer: -1,142.86 feet/minute.

Answer 2

can you write it in green?

Answer 3

Sure! Here’s the answer in green:

Answer: -1,142.86 feet/minute.

Answer 4

no i mean write the letters in green

Answer 5

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Answer: -1,142.86 feet/minute.

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