Question

A serving size of six cookies contains 4 g of fat, 20 of carbohydrates, and 2 g of protein. If walking 1.0 mile consumes 170 kJ of energy, how many miles must you walk to burn off enough calories to eat six cookies? Assume the energy content of fats, carbohydrates, and proteins are 8 kcallg, 4 kcallg, and 4 kcallg, respectively.

Short answer

A person must walk approximately \(2.95\) miles to burn off enough calories to consume six cookies.

Step-by-step solution

1. Calculate the energy content of six cookies

Multiply the grams of each substance (fat, carbohydrates, and protein) by its corresponding energy content (kcal/g) and add them all up to find the total energy content of six cookies in kcal. Energy_of_cookies = (4 g * 8 kcal/g) + (20 g * 4 kcal/g) + (2 g * 4 kcal/g)

2. Convert the energy content to kJ

Use the conversion factor 1 kcal = 4.184 kJ to convert the energy content of six cookies from kcal to kJ. Energy_of_cookies_kJ = Energy_of_cookies * 4.184 kJ/kcal

3. Calculate the number of miles to walk

Divide the total energy content of six cookies (in kJ) by the energy consumed from walking 1 mile (170 kJ) to find out how many miles a person must walk to burn off the calories. Miles_to_walk = Energy_of_cookies_kJ / 170 kJ/mile Perform the calculations: Energy_of_cookies = (4 g * 8 kcal/g) + (20 g * 4 kcal/g) + (2 g * 4 kcal/g) = 32 kcal + 80 kcal + 8 kcal = 120 kcal Energy_of_cookies_kJ = 120 kcal * 4.184 kJ/kcal = 502.08 kJ Miles_to_walk = 502.08 kJ / 170 kJ/mile ≈ 2.95 miles Therefore, a person must walk approximately 2.95 miles to burn off enough calories to consume six cookies.

Key concepts

Nutrition Calculations

Understanding how to perform nutrition calculations is crucial in managing your diet and energy balance. In the original exercise, we start by identifying the nutritional content of cookies in terms of fats, carbohydrates, and proteins. Each of these macronutrients provides a specific amount of energy:

• Fats: 8 kcal/g
• Carbohydrates: 4 kcal/g
• Proteins: 4 kcal/g

To find out the total energy content, you multiply the grams of each macronutrient by its energy value. For six cookies, it breaks down like this:

• Fat energy: 4 g * 8 kcal/g = 32 kcal
• Carbohydrate energy: 20 g * 4 kcal/g = 80 kcal
• Protein energy: 2 g * 4 kcal/g = 8 kcal

Adding these together gives us the total energy content of 120 kcal for the cookies. This calculation highlights how you can use nutritional information to understand the energy intake from your food.

Energy Conversion

Energy conversion is a fundamental concept, especially when shifting from nutritional analysis to exercise requirements. In this context, energy is initially calculated in kilocalories (kcal). However, to relate this to physical activity, we need to convert it into kilojoules (kJ) because energy expenditure from exercise is often expressed in kJ.
To convert kcal to kJ, use the conversion factor: 1 kcal = 4.184 kJ.So, the total energy from the cookies (120 kcal) becomes:\[120 \text{ kcal} \times 4.184 \frac{\text{kJ}}{\text{kcal}} = 502.08 \text{ kJ}\]By knowing this conversion, you can seamlessly translate the energy you consume into the energy you exert through activities. This understanding is essential for balancing your diet with your physical activity levels.

Exercise and Metabolism

Exercise and metabolism are closely linked when it comes to burning calories. The original problem tells us that walking 1.0 mile consumes 170 kJ of energy. To determine how far you need to walk to burn off the energy from the cookies, you divide the total energy content by the energy burned per mile.Here's the calculation:\[\text{Miles to walk} = \frac{502.08 \text{ kJ}}{170 \text{ kJ/mile}} \approx 2.95 \text{ miles}\]This result means you need to walk nearly 3 miles to neutralize the calorie intake from the cookies. It's crucial to understand that metabolism varies for each individual, affecting how efficiently your body converts consumed energy into work. Additionally, factors such as age, weight, and overall fitness level can influence how much energy you burn during exercise. This understanding helps you tailor your physical activity to your nutritional intake efficiently.