Question
Dahlia hikes 2 14 miles in 12 an hour. At this rate, how long will it take her to walk 18 miles?
4 hours
8 hours
10 hours
12 hours
4 hours
8 hours
10 hours
12 hours
Answers
GPT-4o mini
To determine how long it will take Dahlia to hike 18 miles, we first need to find her hiking speed.
Dahlia walks \(2 \frac{1}{4}\) miles in 12 hours. Converting \(2 \frac{1}{4}\) miles to an improper fraction, we get:
\[
2 \frac{1}{4} = \frac{9}{4} \text{ miles}
\]
Now, we can find her speed in miles per hour (mph) by dividing the distance by the time:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{9}{4} \text{ miles}}{12 \text{ hours}} = \frac{9}{4} \div 12 = \frac{9}{4} \times \frac{1}{12} = \frac{9}{48} = \frac{3}{16} \text{ miles per hour}
\]
Now that we have her speed, let's calculate how long it will take her to walk 18 miles using the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Substituting the values we have:
\[
\text{Time} = \frac{18 \text{ miles}}{\frac{3}{16} \text{ miles per hour}} = 18 \times \frac{16}{3} = \frac{288}{3} = 96 \text{ hours}
\]
Now, let's double-check the calculations:
1. We found that Dahlia’s speed is \( \frac{3}{16} \) miles per hour.
2. To find how long it takes to walk 18 miles:
\[
\text{Time} = \frac{18 \text{ miles}}{\frac{3}{16} \text{ miles per hour}} = 18 \times \frac{16}{3}
\]
Calculating \(18 \times \frac{16}{3}\):
\[
= \frac{288}{3} = 96 \text{ hours}
\]
Therefore, it seems there may have been a misunderstanding of the time or distance provided in the choices.
None of the provided options of 4 hours, 8 hours, 10 hours, or 12 hours are correct based on the calculations. The correct answer should be 96 hours. Please double-check the original problem if necessary.
Dahlia walks \(2 \frac{1}{4}\) miles in 12 hours. Converting \(2 \frac{1}{4}\) miles to an improper fraction, we get:
\[
2 \frac{1}{4} = \frac{9}{4} \text{ miles}
\]
Now, we can find her speed in miles per hour (mph) by dividing the distance by the time:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{9}{4} \text{ miles}}{12 \text{ hours}} = \frac{9}{4} \div 12 = \frac{9}{4} \times \frac{1}{12} = \frac{9}{48} = \frac{3}{16} \text{ miles per hour}
\]
Now that we have her speed, let's calculate how long it will take her to walk 18 miles using the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Substituting the values we have:
\[
\text{Time} = \frac{18 \text{ miles}}{\frac{3}{16} \text{ miles per hour}} = 18 \times \frac{16}{3} = \frac{288}{3} = 96 \text{ hours}
\]
Now, let's double-check the calculations:
1. We found that Dahlia’s speed is \( \frac{3}{16} \) miles per hour.
2. To find how long it takes to walk 18 miles:
\[
\text{Time} = \frac{18 \text{ miles}}{\frac{3}{16} \text{ miles per hour}} = 18 \times \frac{16}{3}
\]
Calculating \(18 \times \frac{16}{3}\):
\[
= \frac{288}{3} = 96 \text{ hours}
\]
Therefore, it seems there may have been a misunderstanding of the time or distance provided in the choices.
None of the provided options of 4 hours, 8 hours, 10 hours, or 12 hours are correct based on the calculations. The correct answer should be 96 hours. Please double-check the original problem if necessary.