Math Problem Statement

Convert all the distances to a single unit

Solution

To convert all the distances to a single unit, let's choose feet as the common unit for uniform comparison. We will convert miles and inches to feet, as some distances are already given in feet.

Conversion Factors:

  • 1 mile = 5280 feet
  • 1 inch = 1/12 feet

Let's convert each distance to feet:

  1. Yellowstone:

    • Feet: 5280 feet
    • Inches: 1200 inches to feet Inches to Feet=120012=100 feet\text{Inches to Feet} = \frac{1200}{12} = 100 \text{ feet}
    • Total Distance in Feet: 5280+100=5380 feet5280 + 100 = 5380 \text{ feet}
  2. Denver:

    • Miles: 1 mile to feet Miles to Feet=1×5280=5280 feet\text{Miles to Feet} = 1 \times 5280 = 5280 \text{ feet}
    • Total Distance in Feet: 5280 feet5280 \text{ feet}
  3. Austin:

    • Feet: 144 feet
    • Total Distance in Feet: 144 feet144 \text{ feet}
  4. Branson:

    • Feet: 1200 feet
    • Total Distance in Feet: 1200 feet1200 \text{ feet}
  5. Outer Banks:

    • Feet: 386 feet
    • Total Distance in Feet: 386 feet386 \text{ feet}
  6. New York City:

    • Inches: 600 inches to feet Inches to Feet=60012=50 feet\text{Inches to Feet} = \frac{600}{12} = 50 \text{ feet}
    • Total Distance in Feet: 50 feet50 \text{ feet}
  7. Maine:

    • Miles: 2 miles to feet Miles to Feet=2×5280=10560 feet\text{Miles to Feet} = 2 \times 5280 = 10560 \text{ feet}
    • Total Distance in Feet: 10560 feet10560 \text{ feet}

Summary of Distances in Feet:

CityDistance in Feet
Yellowstone5380
Denver5280
Austin144
Branson1200
Outer Banks386
New York City50
Maine10560

Would you like any further analysis on these distances or any additional calculations?

Follow-Up Questions:

  1. Would you like to determine the city with the shortest and longest distance?
  2. Are there any specific cities you are interested in comparing?
  3. Would you like to convert these distances to another unit, such as miles or inches?
  4. Are you interested in finding the average distance across all cities?
  5. Would you like to visualize these distances on a graph for better comparison?

Tip:

When comparing distances, consider using both relative and absolute differences to gain more insights into the variations between different locations.

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Math Problem Analysis

Mathematical Concepts

Unit conversion
Distance measurement

Formulas

Conversion of miles to feet
Conversion of inches to feet

Theorems

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Suitable Grade Level

Grades 6-8