To find out how long it takes the tortoise to walk 1 mile when it takes her \( \frac{1}{4} \) hours to walk \( 6 \frac{5}{6} \) miles, you first need to convert \( 6 \frac{5}{6} \) miles into an improper fraction.
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Convert \( 6 \frac{5}{6} \) to an improper fraction: \[ 6 \frac{5}{6} = 6 \times 6 + 5 = 36 + 5 = 41 \quad \text{(miles)} \] So, the tortoise walks \( \frac{1}{4} \) hours to walk \( \frac{41}{6} \) miles.
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To find the time to walk 1 mile, you would divide the distance by the rate (which is the same as finding how many times 1 mile fits into \( \frac{41}{6} \) miles). You can calculate the time taken for 1 mile by knowing that the tortoise walks \( \frac{41}{6} \) miles in \( \frac{1}{4} \) hours:
\[ \text{Time for 1 mile} = \frac{\frac{1}{4} \text{ hours}}{\frac{41}{6} \text{ miles}} \]
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To compute this, you can multiply by the reciprocal of the distance:
\[ \text{Time for 1 mile} = \frac{1}{4} \times \frac{6}{41} = \frac{6}{164} = \frac{3}{82} \text{ hours} \]
Thus, the tortoise takes \( \frac{3}{82} \) hours to walk 1 mile.
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