Math Problem Statement
Sarah notices her map has a scale of 1/4 inch = 1 mile. She measures 12.5 inches between Beaver Falls and Chipmonk Cove. How far apart are the cities?
Solution
Let's analyze the problem in the image:
The scale of the map is given as inch = 1 mile. Sarah measures 12.5 inches on the map between Beaver Falls and Chipmonk Cove.
To find the real distance between the cities:
- For every inch on the map, the real-world distance is 1 mile.
- We first convert the measured distance (12.5 inches) into how many -inch units are in 12.5 inches:
Thus, the cities are 50 miles apart.
The correct answer is (c) 50 miles.
Would you like more details or have any further questions on this?
Here are 5 related questions to expand on this concept:
- How would the real distance change if the scale was inch = 1 mile instead?
- How do you convert distances on maps with a metric scale (e.g., cm to km)?
- What is the real distance if Sarah measured 15 inches on the same map?
- How do you calculate the scale factor when given different units like kilometers and miles?
- Can you explain how map projections affect distances on maps?
Tip: When working with scales, always ensure that units are consistent between the measured map distance and the real-world scale.
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Math Problem Analysis
Mathematical Concepts
Ratios and Proportions
Unit Conversion
Formulas
Distance = (Measured inches on map) / (Scale ratio)
Distance = 12.5 / (1/4)
Theorems
Proportionality Theorem
Suitable Grade Level
Grades 6-8