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:

  1. 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.

    1 Calorie=4184 Joules1 \text{ Calorie} = 4184 \text{ Joules}

    So, 104 Calories is equivalent to:

    104×4184=434,944 Joules104 \times 4184 = 434,944 \text{ Joules}

  2. 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):

    8 minutes=8×60=480 seconds8 \text{ minutes} = 8 \times 60 = 480 \text{ seconds}

  3. Calculate the average power output:

    Power is defined as the energy consumed per unit time. In formula terms:

    Power (P)=Energy (E)Time (t)\text{Power (P)} = \frac{\text{Energy (E)}}{\text{Time (t)}}

    Substituting the energy in joules and time in seconds:

    P=434,944 Joules480 secondsP = \frac{434,944 \text{ Joules}}{480 \text{ seconds}}

    Calculating the power:

    P906.13 wattsP \approx 906.13 \text{ watts}

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:

  1. How do you convert calories per minute to watts?
  2. If you run at a different speed, how does it affect your power output?
  3. What factors affect the number of calories burned per mile?
  4. How would you calculate the power output for a different duration of exercise?
  5. 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