Question

A tortoise takes 1 1/4 ​hours to walk 5/6 miles. At this rate, how long does it take her to walk 1 mile?

Answer 1

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.

1. Convert \(1 \frac{1}{4}\) hours into an improper fraction:
\[
1 \frac{1}{4} = \frac{5}{4} \text{ hours}
\]

2. Now, we calculate the rate in miles per hour:
\[
\text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{5}{6} \text{ miles}}{\frac{5}{4} \text{ hours}} = \frac{5}{6} \div \frac{5}{4} = \frac{5}{6} \times \frac{4}{5}
\]

3. 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.

4. Calculate the time to walk 1 mile:
\[
\text{Time} = \frac{1 \text{ mile}}{\frac{2}{3} \text{ miles per hour}} = 1 \times \frac{3}{2} = \frac{3}{2} \text{ hours}
\]

5. 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.