Question

Dahlia hikes 2 1/4 miles in 1/2 an hour. At this rate, how long will it take her to walk 18 miles?
4 hours
8 hours
10 hours
12 hours

Answer 1

First, let's determine Dahlia's hiking rate in miles per hour. She hikes \(2 \frac{1}{4}\) miles in \(\frac{1}{2}\) hour.

Convert \(2 \frac{1}{4}\) miles into an improper fraction:
\[
2 \frac{1}{4} = \frac{9}{4} \text{ miles}
\]

Now, let's find her rate in miles per hour:
\[
\text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{9}{4} \text{ miles}}{\frac{1}{2} \text{ hour}} = \frac{9}{4} \times \frac{2}{1} = \frac{9 \times 2}{4 \times 1} = \frac{18}{4} = \frac{9}{2} \text{ miles per hour}
\]

Next, we want to find out how long it will take her to walk 18 miles. To do this, we will use the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Rate}}
\]

Substituting in the values:
\[
\text{Time} = \frac{18 \text{ miles}}{\frac{9}{2} \text{ miles per hour}} = 18 \times \frac{2}{9} = \frac{36}{9} = 4 \text{ hours}
\]

Thus, it will take Dahlia **4 hours** to walk 18 miles.

The answer is:
\[
\boxed{4 \text{ hours}}
\]