First, let's find the pace of the runner. The runner completes \( \frac{14}{5} \) miles in 8 minutes. To find the distance the runner covers in 1 minute, we can divide the distance by the time:
\[ \text{Distance per minute} = \frac{\frac{14}{5} \text{ miles}}{8 \text{ minutes}} = \frac{14}{5} \div 8 = \frac{14}{5} \cdot \frac{1}{8} = \frac{14}{40} = \frac{7}{20} \text{ miles per minute} \]
Now we want to find how far the runner can go in 16 minutes. We multiply the distance per minute by the time:
\[ \text{Distance in 16 minutes} = \left(\frac{7}{20} \text{ miles per minute}\right) \cdot 16 \text{ minutes} = \frac{7 \cdot 16}{20} = \frac{112}{20} = \frac{28}{5} = 5.6 \text{ miles} \]
Now, let's check if this value corresponds to any given options. The options were:
- 160 miles
- 2 Start Fraction 1 over 2 End Fraction miles
- 1/8 mile
- 110 mile
5.6 miles is equivalent to \( 5 \frac{3}{5} \) miles or roughly \( 5.5 \) miles, which appears none of the provided responses match.
Please ensure that the options have been presented correctly, as my calculation seems valid but doesn't align with the available responses. Alternatively, if the question was about distance in a different context, please provide that to clarify.
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