Assume running consumes 104 Calories per mile. If you run 8​-minute ​miles, what is your average power​ output, in​ watts?

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.

   \[
   1 \text{ Calorie} = 4184 \text{ Joules}
   \]

   So, 104 Calories is equivalent to:

   \[
   104 \times 4184 = 434,944 \text{ Joules}
   \]

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):

   \[
   8 \text{ minutes} = 8 \times 60 = 480 \text{ seconds}
   \]

3. **Calculate the average power output:**

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

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

   Substituting the energy in joules and time in seconds:

   \[
   P = \frac{434,944 \text{ Joules}}{480 \text{ seconds}}
   \]

   Calculating the power:

   \[
   P \approx 906.13 \text{ watts}
   \]

### 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.

Learn how to calculate average power output when running 8-minute miles. This problem involves converting energy from calories to joules, calculating time in seconds, and applying the power formula. Discover the relationship between energy consumption and power output. Suitable for advanced high school and college students.

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