Math Problem Statement

Lane knows that when he runs, he takes about 180 steps per minute and that each step is 3.25 feet long. Which calculation is most reasonable for Lane to use to find out his running speed in miles per hour?

Solution

The problem is asking which calculation is most reasonable for Lane to use in order to convert his running speed into miles per hour, given that:

  • Lane takes 180 steps per minute.
  • Each step is 3.25 feet long.

The task is to determine the correct calculation that converts steps per minute into miles per hour.

Steps for Conversion:

  1. Convert steps to feet: Multiply 180 steps by 3.25 feet per step.
  2. Convert feet to miles: Since 1 mile equals 5,280 feet, divide the result by 5,280 feet to get miles.
  3. Convert minutes to hours: Multiply the result by 60 to convert minutes to hours.

Correct Formula:

The second option in the image looks correct, which is:

180 steps×3.25 feet1 step×1 mile5280 feet×60 minutes1 hour180 \text{ steps} \times \frac{3.25 \text{ feet}}{1 \text{ step}} \times \frac{1 \text{ mile}}{5280 \text{ feet}} \times \frac{60 \text{ minutes}}{1 \text{ hour}}

This calculation correctly multiplies to get miles per hour, using the appropriate unit conversions.

Would you like more details, or do you have any questions about this process?


Here are 5 related questions to expand your understanding:

  1. How can you verify the result of the calculation in miles per hour?
  2. What other units could Lane use to express his speed?
  3. How would the calculation change if Lane took 200 steps per minute instead of 180?
  4. How could you calculate Lane's time to run a specific distance, such as 5 miles?
  5. What other factors, such as terrain or wind, might affect Lane's running speed?

Tip: When performing unit conversions, always make sure units cancel out properly, leaving you with the desired final units!

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Proportions
Multiplication

Formulas

Steps per minute × Feet per step = Feet per minute
Feet per minute ÷ 5280 (feet in a mile) = Miles per minute
Miles per minute × 60 (minutes in an hour) = Miles per hour

Theorems

Unit conversion principles

Suitable Grade Level

Grades 6-8