To find out how many miles Janice walked, we can follow these steps:
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Determine the walking rate: Janice walks at a rate of 1 mile every \( \frac{1}{4} \) hour. To find her speed in miles per hour, we can calculate how many miles she walks in 1 hour: \[ \text{Speed} = \frac{1 \text{ mile}}{\frac{1}{4} \text{ hour}} = 1 \times 4 = 4 \text{ miles per hour}. \]
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Calculate the total time in hours she walked: Janice walked for \( \frac{7}{8} \) hour.
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Calculate the distance she walked: We use the formula: \[ \text{Distance} = \text{Speed} \times \text{Time}. \]
Plugging in the values: \[ \text{Distance} = 4 \text{ miles per hour} \times \frac{7}{8} \text{ hour}. \]
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Multiply the speed by the time: \[ \text{Distance} = 4 \times \frac{7}{8} = \frac{4 \times 7}{8} = \frac{28}{8}. \]
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Simplify the fraction: \[ \frac{28}{8} = \frac{7}{2} = 3 \frac{1}{2}. \]
Thus, Janice walked a total of \( 3 \frac{1}{2} \) miles.
The final answer is: \[ \boxed{3 \frac{1}{2}}. \]