Math Problem Statement

Sound can travel incredibly quickly: 1 mile in about 1/12 of a minute. Based on that, what is the approximate speed of sound? Simplify your answer and write it as a proper fraction, mixed number, or whole number. miles per minute

Solution

The speed of sound can be calculated as follows:

Since sound travels 1 mile in 112\frac{1}{12} of a minute, we want to find the distance traveled in 1 full minute.

Step-by-Step Calculation

  1. Let xx represent the speed of sound in miles per minute.
  2. Since 1 mile is traveled in 112\frac{1}{12} minute, we can write: x=1 mile112 minutex = \frac{1 \text{ mile}}{\frac{1}{12} \text{ minute}}
  3. To simplify, divide 1 by 112\frac{1}{12}: x=1÷112=1×121=12x = 1 \div \frac{1}{12} = 1 \times \frac{12}{1} = 12

Answer

The speed of sound is approximately 12 miles per minute.

Would you like further details on this solution, or have any questions?


Here are 5 related questions to expand on this concept:

  1. How would the speed of sound in miles per hour be calculated from this rate?
  2. If sound traveled 15 miles in 1.25 minutes, what would be its speed in miles per minute?
  3. How would the speed of sound vary at different altitudes or temperatures?
  4. Can we convert this speed into meters per second, using 1 mile ≈ 1,609 meters?
  5. If a sound wave takes 2 minutes to travel 24 miles, what would be its speed?

Tip: Remember that dividing by a fraction is the same as multiplying by its reciprocal.

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Math Problem Analysis

Mathematical Concepts

Algebra
Unit Conversion
Fractions
Rates

Formulas

Speed = Distance / Time
Dividing by a fraction: a ÷ (b/c) = a × (c/b)

Theorems

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Suitable Grade Level

Grades 5-7