Math Problem Statement

The task is to find the real-world distance between the library and the train station using the given map scale: 1 inch = 5 miles.

Solution

I see you've uploaded an image that includes a lesson about using scale to find distances. Let's work through it!

The text reads:

"Develop: Using Scale to Find Distances"

This map is a scale drawing of the streets in a town. The scale from the town map says:
1 inch = 5 miles.

The task is to use the map scale to determine the distance between two locations on the map, specifically the library and the train station.

Solution Steps:

  1. Measure the distance between the library and the train station on the map using a ruler.
  2. Use the given scale 1 inch=5 miles\text{1 inch} = 5 \text{ miles} to convert the measured distance into real-world miles.

For example, if the distance on the map is 2 inches, the real-world distance would be: Distance=2inches×5miles/inch=10miles\text{Distance} = 2 \, \text{inches} \times 5 \, \text{miles/inch} = 10 \, \text{miles}

If you provide the measurement (or if you want me to estimate based on the image), I can assist with the calculation.

Would you like more details or further clarification on this?
Here are five related questions you could explore further:

  1. What other units of measurement could be used for scaling besides inches and miles?
  2. How can you determine the scale of a map when it's not provided?
  3. What would happen if the scale were 1inch=10miles1 \, \text{inch} = 10 \, \text{miles}? How would this change the calculation?
  4. How is scale used in real-world applications like architecture or city planning?
  5. How could you use this concept to estimate travel time between two locations?

Tip: When using a scale, make sure the units on the map match the units you're working with in real life (e.g., miles, kilometers).

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Math Problem Analysis

Mathematical Concepts

Scale factor
Distance calculation
Measurement conversion

Formulas

Real-world distance = Measured distance × Scale factor

Theorems

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Suitable Grade Level

Grade 6-8