Math Problem Statement

A road map has a scale of 1:50,000. The length of a road on the map is 8.5 cm. Work out the length of the real road in kilometers.

Solution

To solve the problem:

Problem Breakdown:

The map has a scale of 1:50,000, meaning 1 cm on the map corresponds to 50,000 cm in real life.
The given length of the road on the map is 8.5 cm.

Conversion Steps:

  1. Convert the map length into real-world length: Real length in cm=8.5×50,000=425,000cm.\text{Real length in cm} = 8.5 \times 50,000 = 425,000 \, \text{cm}.

  2. Convert the real-world length from centimeters to kilometers: 1km=100,000cm.1 \, \text{km} = 100,000 \, \text{cm}. Therefore: Real length in km=425,000100,000=4.25km.\text{Real length in km} = \frac{425,000}{100,000} = 4.25 \, \text{km}.

Final Answer:

The real length of the road is 4.25 kilometers.

Let me know if you’d like a detailed explanation of the steps or assistance with another question!


Follow-up Questions to Enhance Understanding:

  1. What would the real length be if the road on the map measured 10 cm?
  2. How does changing the scale to 1:100,000 affect the real-world calculation?
  3. How do we convert real lengths to map lengths given a specific scale?
  4. What units are most convenient for large-scale conversions, and why?
  5. How can map scales be used to calculate areas in real-world dimensions?

Tip: Always double-check the scale units (e.g., cm, km

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Math Problem Analysis

Mathematical Concepts

Scales and ratios
Unit conversion
Proportional reasoning

Formulas

Real length = map length × scale factor
1 kilometer = 100,000 centimeters

Theorems

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Suitable Grade Level

Grades 6-8