To determine how long it takes the tortoise to walk 1 mile, we can first find the tortoise's walking rate in miles per hour.
The tortoise takes \(1 \frac{1}{4}\) hours to walk \( \frac{5}{6} \) miles.
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Convert \(1 \frac{1}{4}\) hours into an improper fraction: \[ 1 \frac{1}{4} = \frac{5}{4} \text{ hours} \]
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Now, we calculate the rate in miles per hour: \[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{5}{6} \text{ miles}}{\frac{5}{4} \text{ hours}} = \frac{5}{6} \div \frac{5}{4} = \frac{5}{6} \times \frac{4}{5} \]
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Simplify: \[ \frac{5 \times 4}{6 \times 5} = \frac{4}{6} = \frac{2}{3} \text{ miles per hour} \]
Now that we know the tortoise's speed is \( \frac{2}{3} \) miles per hour, we can find the time it takes to walk 1 mile using the formula time = distance / rate.
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Calculate the time to walk 1 mile: \[ \text{Time} = \frac{1 \text{ mile}}{\frac{2}{3} \text{ miles per hour}} = 1 \times \frac{3}{2} = \frac{3}{2} \text{ hours} \]
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Convert \( \frac{3}{2} \) hours into hours and minutes: \[ \frac{3}{2} \text{ hours} = 1 \text{ hour} , 30 \text{ minutes} \]
Thus, it takes the tortoise 1 hour and 30 minutes to walk 1 mile.