To solve the problem, we first need to determine the runner's pace based on the information given.
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Determine the distance covered every 8 minutes: The runner completes \( \frac{1}{4} \) of a 5-mile race in 8 minutes. \[ \frac{1}{4} \text{ of } 5 \text{ miles} = \frac{5}{4} \text{ miles} = 1.25 \text{ miles} \]
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Determine the runner's speed in miles per minute: Since the runner covers \( 1.25 \) miles in 8 minutes, we can find the speed by calculating: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{1.25 \text{ miles}}{8 \text{ minutes}} = 0.15625 \text{ miles per minute} \]
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Calculate the distance covered in 16 minutes: Now, we multiply the speed by 16 minutes to find out how far the runner can go in that time. \[ \text{Distance} = \text{Speed} \times \text{Time} = 0.15625 \text{ miles/min} \times 16 \text{ minutes} = 2.5 \text{ miles} \]
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Convert miles to a fraction if needed: Since \( 2.5 \) miles can be written as \( \frac{5}{2} \) miles, but let's ensure if this corresponds to the options provided.
However, none of the provided choices (1/8 mile, 160 miles, 1/10 mile, 2/12 miles) include \( \frac{5}{2} \) miles.
It's possible that I've misunderstood the problem or need to check if the choices provided are accurate. But based on the calculations done:
- The runner can go 2.5 miles in 16 minutes.
The closest standard fraction representation of 2.5 is: \[ \frac{5}{2} \text{ miles} = 2.5 \text{ miles} \]
But this was not among the options provided. Therefore, it appears there might be an issue with the answer choices themselves.