Going Round-Trip with the World’s Fastest Land Animal

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- If the cheetah made a round-trip and took half the amount of time on the return trip as on the front end of the trip, what would be the relationship between the average rates on each leg of the trip? Using a complete sentence, explain how you arrived at this conclusion.

The relationship would be 2:1. Which means the cheetah went twice as fast on the return trip.

Step 3: Calculating time

Assume that the cheetah travels an average of 40 mph to go from its resting place to a rock near a river. On the return trip to its resting place, the cheetah travels an average of 70 mph. If the cheetah traveled for 15 minutes, how many minutes did the return trip take to the nearest minute and second?

- Set up the table as follows. Label the rows “To the River” and “From the River.” Label the columns “Distance,” “Rate,” and “Time (in Hours).” Let t represent the unknown quantity in the problem. Fill in the table.

Distance

Rate

Time

(in hours)

To the River

40mph

From the River

70mph

- From the table, set up an equation relating the distances.

- Solve the problem. Write the answer in a complete sentence, stating it in terms of minutes and seconds.

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?

- The average rate for the trip is equal to the total distance traveled divided by the total time traveled. The following equations represent the distance traveled on each leg of the trip.

First leg of trip: [pic 1]

Second leg of trip: [pic 2]

Write an equation for the average rate for the trip. Remember, the cheetah runs from point A to point B and back to point A.

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- The following equation represents the average rate for the trip. Is this equation equivalent to the one you wrote above? Explain why or why not.

[pic 3]

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- The following steps show how the equation for the average rate can be transformed so that it is written in terms of only the rates for each leg of the trip. Write an algebraic justification for each step. Think about the number operations and properties that you know.

[pic 4]

[pic 5]

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[pic 6]

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[pic 7]

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- Using the equation for average rate above, determine the cheetah’s average rate for the entire trip.