The scale of a map is `1:3xx10^7`. Two cities are 5 cm apart on the map. Find the actual distance between them in kilometers.

Options

A. `1350 km`
B. `1450 km`
C. `1550 km`
D. `1500 km`

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Understand the scale of the map
The scale of the map is given as \(1 : 3 \times 10^7\). This means that 1 cm on the map represents \(3 \times 10^7\) cm in reality.

### Step 2: Identify the distance on the map
The distance between the two cities on the map is given as 5 cm.

### Step 3: Set up the proportion
We can use the scale to set up the proportion:
\[ \frac{1 \text{ cm (map distance)}}{3 \times 10^7 \text{ cm (actual distance)}} = \frac{5 \text{ cm (map distance)}}{x \text{ cm (actual distance)}} \]
Where \(x\) is the actual distance we want to find.

### Step 4: Cross-multiply to solve for \(x\)
Cross-multiplying gives us:
\[ 1 \cdot x = 5 \cdot (3 \times 10^7) \]
So,
\[ x = 5 \cdot 3 \times 10^7 \]

### Step 5: Calculate \(x\)
Now, calculate \(x\):
\[ x = 15 \times 10^7 \text{ cm} \]

### Step 6: Convert centimeters to kilometers
To convert centimeters to kilometers, we use the conversion factor \(1 \text{ cm} = 10^{-5} \text{ km}\). Thus,
\[ x \text{ (in km)} = 15 \times 10^7 \text{ cm} \times 10^{-5} \text{ km/cm} \]
This simplifies to:
\[ x = 15 \times 10^{7 - 5} \text{ km} = 15 \times 10^2 \text{ km} \]

### Step 7: Final calculation
Calculating \(15 \times 10^2\):
\[ x = 1500 \text{ km} \]

### Conclusion
The actual distance between the two cities is **1500 kilometers**.

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