To find out how long it takes the tortoise to walk 1 mile, you need to divide the total time it takes to walk 6.5 miles by the distance of 6.5 miles.
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First, let's convert \(6\frac{1}{2}\) miles into an improper fraction or decimal.
- \(6\frac{1}{2} = 6.5\)
- \(6.5\) can be expressed as \(\frac{13}{2}\).
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The tortoise takes \(\frac{1}{4}\) hours to walk this distance.
Now, to find the time it takes to walk 1 mile, you can set up the following equation, where \(x\) is the time (in hours) taken to walk 1 mile:
\[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} \]
So the rate at which the tortoise walks is: \[ \frac{6.5 \text{ miles}}{\frac{1}{4} \text{ hours}} = 6.5 \div \frac{1}{4} = 6.5 \times 4 = 26 \text{ miles per hour} \]
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To find the time to walk 1 mile, you take the reciprocal of the rate: \[ \text{Time for 1 mile} = \frac{1 \text{ mile}}{\text{Rate}} = \frac{1}{26} \text{ hours} \]
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Alternatively, you can also find the time for 1 mile directly from the total: \[ \text{Time for 1 mile} = \frac{\frac{1}{4} \text{ hours}}{6.5 \text{ miles}} = \frac{1}{4} \div 6.5 = \frac{1}{4} \times \frac{1}{6.5} = \frac{1}{26} \text{ hours} \]
Thus, the tortoise takes \(\frac{1}{26}\) hours to walk 1 mile.
The value you need to divide \(6.5\) miles by to find \(1\) mile is \(6.5\).
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