To determine which statement best describes the rates of Charlie and Kyle, we need to analyze both runners' rates as presented in the problem.
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Kyle's Rate: The function representing Kyle's practice times is given by the equation \( y = 7.5x \). This means that Kyle runs 7.5 miles per hour.
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Charlie's Rate: Charlie's rates are represented on a graph. Without the exact details from the graph provided, we can only evaluate based on the options given.
To examine the options, let's denote Charlie's rate as \( C \) miles per hour.
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Option A states that Kyle's rate is 1.5 miles per hour greater than Charlie's rate. Mathematically, this means that \( 7.5 = C + 1.5 \), leading to \( C = 6.0 \). If Charlie runs at 6.0 miles per hour, this option could be true.
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Option B states Charlie's rate is 1 mile per hour greater than Kyle's rate, meaning \( C = 7.5 + 1 = 8.5 \). But since Kyle runs 7.5 miles per hour, this is not possible.
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Option C indicates Kyle's rate is 1.5 miles per hour greater than Charlie's. Using the same logic as in option A, this leads to \( 7.5 = C + 1.5 \) or \( C = 6.0 \), making this option potentially valid.
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Option D asserts that both runners have the same rate. Since Kyle runs at 7.5 miles per hour, this option cannot be true unless Charlie's rate is also 7.5, which contradicts options A and C.
Based on this analysis, if we take option A (Kyle's rate is 1.5 miles per hour greater than Charlie's rate) as true, Charlie's rate would be 6.0 miles per hour, which is consistent.
Thus, the best description from the provided options would be:
A Kyle's rate is 1.5 miles per hour greater than Charlie's rate.
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