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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 trip what woul

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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 trip what would be the relationship between the average rates on each leg of the trip

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Answer to a math question If the cheetah made a round trip and took half the amount of time on the return trip as on the front end of trip what would be the relationship between the average rates on each leg of the trip

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\text{1. Define variables for average speeds:}

v_f \text{ for the front trip and } v_r \text{ for the return trip.}

\text{2. Given that the return trip took half the time of the front trip:}

t_r = \frac{t_f}{2}

\text{3. Use the relationship between distance, speed, and time:}

d = v_f \cdot t_f \quad \text{(front trip)}

d = v_r \cdot t_r \quad \text{(return trip)}

\text{4. Since the distances are equal:}

v_f \cdot t_f = v_r \cdot \frac{t_f}{2}

\text{5. Simplify to find the relationship between the speeds:}

v_f = \frac{v_r}{2} \Rightarrow v_r = 2v_f

\text{6. Therefore, the average speed on the return trip is twice the average speed on the front trip:}

v_r = 2v_f

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