To solve the problem, we first need to determine the runner's pace in terms of miles per minute.
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The runner completes \( \frac{1}{4} \) of a 5-mile race every 8 minutes. \[ \frac{1}{4} \text{ of 5 miles} = \frac{5}{4} \text{ miles} = 1.25 \text{ miles} \] Therefore, the runner covers 1.25 miles in 8 minutes.
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To find the pace in miles per minute, we divide the distance covered by the time taken. \[ \text{Pace} = \frac{1.25 \text{ miles}}{8 \text{ minutes}} = 0.15625 \text{ miles per minute} \]
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Next, we want to find out how far the runner can go in 16 minutes at this pace. \[ \text{Distance in 16 minutes} = 0.15625 \text{ miles/minute} \times 16 \text{ minutes} \] \[ = 2.5 \text{ miles} \]
Thus, the runner can go 2½ miles in 16 minutes.
The closest choice from the options given is 2 Start Fraction 1 over 2 End Fraction miles.