Question

Dani's house is 2 and 3-fourths miles from the park. Benjamin's house is 1-third of the way from Dani's house to the park. Dani meets Benjamin at his house. Then, they walk to the park and back to Benjamin's house.

Question
What is the total distance to and from the park that Benjamin walks? Move numbers to the boxes to show the answer. If there is no whole number, place a 0 in the first box.

Response area with 3 blank spaces
Blank space 1 empty

Blank space 2 empty

miles

Blank space 3 empty

Answer 1

To determine the total distance Benjamin walks to and from the park, we first need to calculate the distance from Dani's house to the park and then find out how far Benjamin's house is from the park.

1. **Distance from Dani's house to the park**:
- Dani's house is 2 and 3/4 miles from the park.
- As a mixed number, this can be converted to an improper fraction:
\[
2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \text{ miles}
\]

2. **Benjamin's distance from Dani's house to the park**:
- Benjamin's house is 1/3 of the way from Dani's house to the park. To find this distance:
\[
\text{Distance from Dani's house to the park} = \frac{1}{3} \times \frac{11}{4}
\]
- To calculate:
\[
\frac{1 \times 11}{3 \times 4} = \frac{11}{12} \text{ miles}
\]

3. **Distance from Benjamin's house to the park**:
- The distance from Benjamin’s house to the park is:
\[
\text{Distance from Dani's house to the park} - \text{Distance from Dani's house to Benjamin's house}
\]
- So:
\[
\frac{11}{4} - \frac{11}{12}
\]

- To subtract these fractions, we need a common denominator, which is 12:
\[
\frac{11}{4} = \frac{33}{12} \text{ (multiply numerator and denominator by 3)}
\]
- Now we can subtract:
\[
\frac{33}{12} - \frac{11}{12} = \frac{22}{12} = \frac{11}{6} \text{ miles}
\]

4. **Total distance Benjamin walks**:
- Benjamin walks to the park and then back to his house. Therefore, the total distance is:
\[
2 \times \frac{11}{6} = \frac{22}{6} = \frac{11}{3} \text{ miles}
\]
- Converting \(\frac{11}{3}\) to a mixed number:
\[
\frac{11}{3} = 3 \frac{2}{3}
\]

Now, we can fill in the response area with the results:

**Response area with 3 blank spaces**:
- **Blank space 1**: 3
- **Blank space 2**: 2
- **Blank space 3**: 3 miles

So, the final answer to input is:
```
Blank space 1: 3
Blank space 2: 2
Blank space 3: 3
```