Question
Town Town Actual Distance Between Towns
Bellstown Lewis City 120 km
Bellstown Jenkinsville 40 km
Jenkinsville Lewis City 60 km
Arturo creates a scale drawing showing these distances. If the distance between Lewis City and Bellstown is 6 centimeters on his drawing, how far apart are Lewis City and Jenkinsville on Arturo’s drawing?
(1 point)
Responses
2 centimeters
2 centimeters
3 centimeters
3 centimeters
0.05 centimeters
0.05 centimeters
12 centimeters
Answers
GPT-4o mini
To solve this problem, we need to determine the scale of Arturo's drawing based on the actual distance between Bellstown and Lewis City, and then apply that scale to find the distance between Lewis City and Jenkinsville.
1. **Determine the scale:**
The actual distance between Bellstown and Lewis City is 120 km, which corresponds to 6 centimeters on the drawing.
We can compute the scale as follows:
\[
\text{Scale} = \frac{\text{Drawing Distance (cm)}}{\text{Actual Distance (km)}} = \frac{6 \text{ cm}}{120 \text{ km}} = \frac{1 \text{ cm}}{20 \text{ km}}
\]
So, 1 cm on the drawing represents 20 km in reality.
2. **Find the distance between Jenkinsville and Lewis City:**
The actual distance between Jenkinsville and Lewis City is 60 km.
To find the distance on the drawing, we can use the scale:
\[
\text{Drawing Distance (cm)} = \frac{\text{Actual Distance (km)}}{\text{Scale Factor (km/cm)}}
\]
\[
\text{Drawing Distance (cm)} = \frac{60 \text{ km}}{20 \text{ km/cm}} = 3 \text{ cm}
\]
Therefore, the distance between Lewis City and Jenkinsville on Arturo's drawing is **3 centimeters**.
The correct response is:
**3 centimeters**.
1. **Determine the scale:**
The actual distance between Bellstown and Lewis City is 120 km, which corresponds to 6 centimeters on the drawing.
We can compute the scale as follows:
\[
\text{Scale} = \frac{\text{Drawing Distance (cm)}}{\text{Actual Distance (km)}} = \frac{6 \text{ cm}}{120 \text{ km}} = \frac{1 \text{ cm}}{20 \text{ km}}
\]
So, 1 cm on the drawing represents 20 km in reality.
2. **Find the distance between Jenkinsville and Lewis City:**
The actual distance between Jenkinsville and Lewis City is 60 km.
To find the distance on the drawing, we can use the scale:
\[
\text{Drawing Distance (cm)} = \frac{\text{Actual Distance (km)}}{\text{Scale Factor (km/cm)}}
\]
\[
\text{Drawing Distance (cm)} = \frac{60 \text{ km}}{20 \text{ km/cm}} = 3 \text{ cm}
\]
Therefore, the distance between Lewis City and Jenkinsville on Arturo's drawing is **3 centimeters**.
The correct response is:
**3 centimeters**.