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e)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. in terms of t minutes running at maximum speed. Remember, units of distance and time must agree. Use the conversion information from the warm-up to write a rate in miles per minute.

Respuesta :

Let's denote the speed of the cheetah as v. The distance traveled is the product of speed and time (distance = speed × time). Therefore, for the front end of the trip, the distance is v * t, and for the return trip, the distance is v * (t/2).

Now, let's express the average rate as the total distance divided by the total time. The total distance is 2 * v * t (round trip), and the total time is t + t/2.

Average rate = Total distance / Total time

= (2 * v * t) / (t + t/2)

To simplify, we can multiply the numerator and denominator by 2 to eliminate the fraction:

Average rate = (4 * v * t) / (2t + t)

= (4 * v * t) / (3t)

Now, cancel out the common factor of t:

Average rate = 4v / 3

Therefore, the relationship between the average rates on each leg of the trip is that the rate on the front end is 4/3 times the rate on the return trip. This implies that the cheetah's average speed is faster on the front end of the trip compared to the return leg.

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