The scale of a map is 1 : 2500000. What is the actual distance between two towns if they are 3 cm apart on the map ?

Answer

To find the actual distance between two towns that are 3 cm apart on a map with a scale of 1:2,500,000, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Scale**: The scale of the map is given as 1:2,500,000. This means that 1 unit on the map corresponds to 2,500,000 units in reality.

2. **Identify the Distance on the Map**: The distance between the two towns on the map is given as 3 cm.

3. **Set Up the Proportion**: We can set up a proportion based on the scale. Let \( x \) be the actual distance in centimeters. The proportion can be written as:
\[ \frac{1 \text{ cm (map)}}{2,500,000 \text{ cm (actual)}} = \frac{3 \text{ cm (map)}}{x \text{ cm (actual)}} \]

4. **Cross-Multiply**: To find \( x \), we can cross-multiply:
\[ 1 \cdot x = 3 \cdot 2,500,000 \]
This simplifies to:
\[ x = 3 \times 2,500,000 \]

5. **Calculate \( x \)**: Now, calculate the value of \( x \):
\[ x = 7,500,000 \text{ cm} \]

6. **Convert to Kilometers**: Since the actual distance is required in kilometers, we convert centimeters to kilometers. We know that:
\[ 1 \text{ km} = 100,000 \text{ cm} \]
Therefore, to convert \( 7,500,000 \text{ cm} \) to kilometers:
\[ \text{Distance in km} = \frac{7,500,000 \text{ cm}}{100,000 \text{ cm/km}} = 75 \text{ km} \]

7. **Final Answer**: The actual distance between the two towns is:
\[ \text{Distance} = 75 \text{ km} \]