Question

the table shows how far a distance runner has traveled since the race began. what is her average rate of change, in miles per hour, during the interval 0.75 to 1.00 hours?

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$$\begin{tabular}{|c|c|} \\hline \\text{time elapsed (hours)} & \\text{miles traveled (miles)} \\\\ \\hline 0.50 & 2.00 \\\\ \\hline 0.75 & 3.50 \\\\ \\hline 1.00 & 4.75 \\\\ \\hline \\end{tabular}$$

• 4.75 miles per hour
• 5.00 miles per hour
• 5.50 miles per hour
• 6.00 miles per hour

Explanation:

Identify the values for the given interval

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$$

Calculate the average rate of change

$$ \text{Rate} = \frac{y_2 - y_1}{t_2 - t_1} = \frac{4.75 - 3.50}{1.00 - 0.75} = \frac{1.25}{0.25} = 5.00 $$

Answer:

• (A) 4.75 miles per hour
• (B) 5.00 miles per hour (Correct answer)
• (C) 5.50 miles per hour
• (D) 6.00 miles per hour