Math Problem Statement
Assume running consumes 104 Calories per mile. If you run 8-minute miles, what is your average power output, in watts?
Solution
To calculate the average power output in watts, we first need to understand the relationship between energy consumption (calories burned), time, and power.
Step-by-step Solution:
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Determine the energy consumed:
Given that running consumes 104 calories per mile, we first convert calories to joules because the SI unit of energy is the joule.
So, 104 Calories is equivalent to:
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Calculate the time taken to run one mile:
We are told that it takes 8 minutes to run one mile. To convert this to seconds (since the SI unit of time is seconds):
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Calculate the average power output:
Power is defined as the energy consumed per unit time. In formula terms:
Substituting the energy in joules and time in seconds:
Calculating the power:
Answer:
The average power output is approximately 906 watts.
Would you like a more detailed explanation, or do you have any further questions?
Related Questions:
- How do you convert calories per minute to watts?
- If you run at a different speed, how does it affect your power output?
- What factors affect the number of calories burned per mile?
- How would you calculate the power output for a different duration of exercise?
- What is the relationship between metabolic rate and power output?
Tip: When converting energy units, always keep track of the conversion factors to ensure accuracy in your calculations.
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Math Problem Analysis
Mathematical Concepts
Energy Conversion
Power Calculation
Unit Conversion
Formulas
Power = Energy / Time
Theorems
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Suitable Grade Level
Advanced High School to College