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 14\frac{1}{4} 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:

  1. For every 14\frac{1}{4} inch on the map, the real-world distance is 1 mile.
  2. We first convert the measured distance (12.5 inches) into how many 14\frac{1}{4}-inch units are in 12.5 inches: Number of units=12.5 inches14 inch/unit=12.5×4=50 miles.\text{Number of units} = \frac{12.5 \text{ inches}}{\frac{1}{4} \text{ inch/unit}} = 12.5 \times 4 = 50 \text{ miles}.

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:

  1. How would the real distance change if the scale was 12\frac{1}{2} inch = 1 mile instead?
  2. How do you convert distances on maps with a metric scale (e.g., cm to km)?
  3. What is the real distance if Sarah measured 15 inches on the same map?
  4. How do you calculate the scale factor when given different units like kilometers and miles?
  5. 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