To accurately determine which statement best describes the rates of the runners, we need to analyze the rates of each runner based on their practice times and the provided function for Kyle.
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Kyle's Rate: Kyle's practice times are described by the linear function \( y = 7.5x \). This means that for every hour (x), Kyle runs 7.5 miles (y). Therefore, Kyle's rate is 7.5 miles per hour.
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Charlie's Rate: To compare rates, we need to know Charlie's rate of running. Since Charlie's practice times are represented on a graph, we can find his rate by calculating the slope of the line that represents his practice times. The slope represents the rate of miles per hour.
If we assume that the graph indicates a consistent rate, let's denote Charlie's rate as \( C \). If Kyle's rate is given, we can make comparisons.
Now let's examine the given statements:
- A states that Kyle's rate is 1.5 miles per hour greater than Charlie's. This would be true if Charlie's rate were \( 7.5 - 1.5 = 6 \) miles per hour.
- B claims Charlie's rate is 1 mile per hour greater than Kyle's. This would be true if Charlie's rate were \( 7.5 + 1 = 8.5 \) miles per hour.
- C suggests Kyle's rate is \( \frac{1}{2} \) mile per hour greater than Charlie's. This would be true if Charlie's rate were \( 7.5 - 0.5 = 7 \) miles per hour.
- D indicates that the rates are the same, which would require Charlie's rate to be \( 7.5 \) miles per hour.
Without the specific details from the graph showing Charlie's running times, we cannot definitively state which statement is correct. You would need to calculate or estimate Charlie's rate based on the graph in order to choose one of the given statements.
If you can provide Charlie's specific rate from the graph or more information about the graph, I can help you select the correct answer.
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