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Step 4: Calculating the average rate

Now it’s time to tackle the original question.
Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph.
Can we say that this cheetah’s average rate was 55 mph?

Step 4: Calculating the average rate Now it’s time to tackle the original question-example-1
Step 4: Calculating the average rate Now it’s time to tackle the original question-example-1
Step 4: Calculating the average rate Now it’s time to tackle the original question-example-2
Step 4: Calculating the average rate Now it’s time to tackle the original question-example-3
User Becky
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1 Answer

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Answer: No, we cannot say that the cheetah’s average rate was 55 mph. The average rate of change is not the same as the arithmetic mean of the rates. The average rate of change depends on the distance and time travelled in each direction, not just the rates. To find the average rate of change, we need to use this formula:

Average rate of change = Total distance / Total time

The total distance is the sum of the distances travelled in both directions, which is 2d, where d is the distance from point A to point B. The total time is the sum of the times taken in both directions, which is d/70 + d/40, using the rates given. Simplifying, we get:

Average rate of change = 2d / (d/70 + d/40) = 2800 / (17d)

To get a numerical value for the average rate of change, we need to know the value of d, which is not given in the question. However, we can see that the average rate of change will be less than 55 mph, because 2800 / (17d) < 55 for any positive value of d.

User Szx
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