https://file.aiquickdraw.com/mathbot/file/1727090528839sz8bguqn.jpg

In this problem, we are given the following information:

1. The scale of the drawing is \( \frac{1}{4} \) inch = 3 miles.
2. We need to determine the distance between Hawthorne and Doylestown based on the ruler provided.

### Step-by-step solution:

1. First, we observe the length between Hawthorne and Doylestown on the ruler in inches.
   - From the image, it looks like the distance between Hawthorne and Doylestown is exactly 2¼ inches (2.25 inches).

2. Now, we use the given scale:
   - Every \( \frac{1}{4} \) inch represents 3 miles.
   - To convert inches to miles, we need to calculate how many quarters of an inch are in 2.25 inches:
     \[
     2.25 \text{ inches} = 2.25 \times 4 = 9 \text{ quarters of an inch.}
     \]
3. Since each quarter-inch represents 3 miles, we multiply:
   \[
   9 \times 3 = 27 \text{ miles.}
   \]

Thus, the distance between Hawthorne and Doylestown is **27 miles**, corresponding to option **C**.

Would you like more details or have any questions?

### Follow-up Questions:
1. What would be the distance if the scale was \( \frac{1}{4} \) inch = 4 miles instead?
2. How many miles would the distance be if the ruler showed 3 inches between the two locations?
3. If the distance in miles was given as 30 miles, how many inches would that be on the drawing?
4. What if the scale was changed to \( \frac{1}{2} \) inch = 5 miles, what would the new distance be?
5. How would the calculation change if the distance on the ruler was 1.75 inches?

### Tip:
Always double-check the scale conversions and be sure to multiply or divide properly based on the units provided.

If the scale in the drawing is 1/4 inch = 3 miles, what is the distance, in miles, between Hawthorne and Doylestown?

Learn how to calculate the distance between Hawthorne and Doylestown using a scale of 1/4 inch = 3 miles. This problem involves key mathematical concepts like measurement conversion and proportionality, and is suitable for students in Grades 6-8.

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