To solve the problem, we first need to determine the runner's pace based on the information given. The runner completes \( \frac{1}{4} \) of a 5-mile race in 8 minutes.
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Calculate the distance covered in 8 minutes: \[ \text{Distance completed in 8 minutes} = \frac{1}{4} \times 5 \text{ miles} = \frac{5}{4} \text{ miles} = 1.25 \text{ miles} \]
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Determine the runner's pace (miles per minute): \[ \text{Pace} = \frac{\text{Distance}}{\text{Time}} = \frac{1.25 \text{ miles}}{8 \text{ minutes}} = 0.15625 \text{ miles per minute} \]
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Calculate the distance the runner can cover in 16 minutes: \[ \text{Distance in 16 minutes} = \text{Pace} \times \text{Time} = 0.15625 \text{ miles per minute} \times 16 \text{ minutes} = 2.5 \text{ miles} \]
Therefore, at the same pace, the runner can cover 2.5 miles in 16 minutes.
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