To solve this problem, we need to determine how far the runner can go in 16 minutes if they complete \( \frac{1}{4} \) of a 5-mile race every 8 minutes.
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Find the runner's speed:
- The runner completes \( \frac{1}{4} \) of a 5-mile race every 8 minutes.
- \( \frac{1}{4} \) of 5 miles is \( \frac{5}{4} = 1.25 \) miles in 8 minutes.
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Calculate the speed in miles per minute:
- Speed = Distance / Time = \( \frac{1.25 \text{ miles}}{8 \text{ minutes}} \)
- This simplifies to \( \frac{1.25}{8} \) miles per minute.
- Therefore, speed \( = 0.15625 \) miles per minute.
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Calculate distance in 16 minutes:
- Now, we find the distance the runner can cover in 16 minutes.
- Distance = Speed × Time = \( 0.15625 \text{ miles/min} \times 16 \text{ min} \)
- Distance = \( 2.5 \) miles.
Thus, the runner can go 2.5 miles in 16 minutes. However, the closest option provided is 212 miles, which seems like it could be a typographical error, as it exceeds 5 miles by a significant margin. The correct distance based on our calculations is indeed 2.5 miles.