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

Solution

Given that sound travels 1 mile in 112\frac{1}{12} of a minute, we need to find the speed of sound in miles per minute and then convert it to miles per hour.

Step-by-Step Solution

  1. Find the speed in miles per minute:

    If sound travels 1 mile in 112\frac{1}{12} of a minute, we can find the speed in miles per minute by taking the reciprocal of 112\frac{1}{12}: Speed in miles per minute=1112=12 miles per minute\text{Speed in miles per minute} = \frac{1}{\frac{1}{12}} = 12 \text{ miles per minute}

  2. Convert the speed to miles per hour:

    There are 60 minutes in an hour, so to find the speed in miles per hour, we multiply the speed in miles per minute by 60: Speed in miles per hour=12 miles per minute×60 minutes per hour=720 miles per hour\text{Speed in miles per hour} = 12 \text{ miles per minute} \times 60 \text{ minutes per hour} = 720 \text{ miles per hour}

Simplified Answer

The approximate speed of sound is 720720 miles per hour.

Would you like more details or have any questions?

Here are 5 related questions:

  1. How does the speed of sound change with temperature?
  2. What are the typical speeds of sound in different media like water and steel?
  3. How is the speed of sound measured in scientific experiments?
  4. What is the speed of sound in kilometers per hour?
  5. How does altitude affect the speed of sound?

Tip: The speed of sound varies with the medium it travels through; it is faster in solids and liquids compared to gases.

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Math Problem Analysis

Mathematical Concepts

Proportions
Speed Calculation
Unit Conversion

Formulas

Speed = Distance / Time
Speed in miles per minute = 1 / (1/12) = 12 miles per minute
Speed in miles per hour = Speed in miles per minute * 60

Theorems

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Suitable Grade Level

Grades 6-8