Math Problem Statement

James knows that when he walks, he takes about 120 steps per minute and that each step is 2.75 feet long. Which calculation is most reasonable for James to use to find out his walking speed in miles per hour?

Solution

The problem asks to calculate James' walking speed in miles per hour, given that he takes 120 steps per minute, and each step is 2.75 feet long.

To determine the correct calculation, we need to convert James' walking speed from steps per minute to miles per hour. Here's a breakdown of the reasoning:

  1. Steps per minute to feet per minute:

    • 120steps/min×2.75feet/step=330feet/min120 \, \text{steps/min} \times 2.75 \, \text{feet/step} = 330 \, \text{feet/min}
  2. Convert feet per minute to miles per hour:

    • There are 5,280 feet in a mile and 60 minutes in an hour.
    • So, multiply by 60minutes1hour\frac{60 \, \text{minutes}}{1 \, \text{hour}} to convert minutes to hours, and multiply by 1mile5,280feet\frac{1 \, \text{mile}}{5,280 \, \text{feet}} to convert feet to miles.

The correct setup should look like:

120stepsminute×2.75feetstep×1mile5,280feet×60minutes1hour120 \, \frac{\text{steps}}{\text{minute}} \times 2.75 \, \frac{\text{feet}}{\text{step}} \times \frac{1 \, \text{mile}}{5,280 \, \text{feet}} \times \frac{60 \, \text{minutes}}{1 \, \text{hour}}

This setup matches the second option in the image.

Would you like more details on this solution or have further questions? Here are 5 related questions you can explore:

  1. How do you convert steps per minute into miles per hour?
  2. What is the importance of unit conversion in speed calculations?
  3. How would the result change if James' steps were longer or shorter?
  4. How does multiplying by 60 and dividing by 5,280 help in unit conversion?
  5. How do you apply dimensional analysis in this type of problem?

Tip: Always ensure that your units cancel out properly in conversion problems to get the correct final units.

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Dimensional Analysis
Rate Calculations

Formulas

Steps per minute to feet per minute: 120 steps/min * 2.75 feet/step = 330 feet/min
Feet per minute to miles per hour: 330 feet/min * (1 mile / 5280 feet) * (60 minutes / 1 hour)

Theorems

Dimensional Analysis

Suitable Grade Level

Grade 8