Map Scale Calculation: 1:50,000

This solution calculates the map distance corresponding to a real-world distance using the provided map scale.

Understanding Map Scale 1:50,000

• The scale 1:50,000 means 1 unit on the map represents 50,000 of the same units on the ground.
• Specifically, 1 cm on the map represents 50,000 cm on the ground.

Converting Ground Distance to Centimeters

First, convert the ground distance from kilometers (km) to centimeters (cm).

• Convert km to meters (m): $1.0 \text{ km} = 1.0 \times 1000 \text{ m} = 1000 \text{ m}$
• Convert meters (m) to centimeters (cm): $1000 \text{ m} = 1000 \times 100 \text{ cm} = 100,000 \text{ cm}$
• Therefore, 1.0 km on the ground equals 100,000 cm.

Calculating Map Distance

Use the map scale to find how many centimeters on the map represent 100,000 cm on the ground. Let the map distance be '$x$' cm.

• Set up the proportion using the scale: $ \frac{\text{Map Distance}}{\text{Ground Distance}} = \frac{1}{50,000} $
• Substitute the known values: $ \frac{x \text{ cm}}{100,000 \text{ cm}} = \frac{1}{50,000} $
• Solve for '$x$': $ x = \frac{1}{50,000} \times 100,000 $
• $ x = \frac{100,000}{50,000} $
• $ x = 2 $

Thus, 2 cm on the map represents 1.0 km on the ground.