Question

A 12 -oz can of most colas has about 120 nutritional calories (1 nutritional calorie \(=1\) kilocalorie). Approximately how many minutes of walking are required to burn up as energy the calories taken in after drinking a can of cola? (Walking uses up about \(250 \mathrm{kcal} / \mathrm{h}\).)

Short answer

Answer: Approximately 28.8 minutes.

Step-by-step solution

Write down the given information

We are given the following information: - A can of cola has 120 nutritional calories (which is equal to 120 kcal) - Walking burns 250 kcal/h

Convert walking rate to kcal per minute

Currently, the walking rate is given in kcal per hour. We need to convert it to kcal per minute to match the unit of the final answer. To do this, divide the walking rate by 60 (since there are 60 minutes in an hour): \(\frac{250 \hspace{0.2cm}\mathrm{kcal}}{60\hspace{0.2cm}\mathrm{min}} = 4.167 \hspace{2cm}\mathrm{kcal\,/ \,min}\)

Set up the equation and solve for time

We know that time is equal to the amount of energy used divided by the rate of energy consumption. The equation we can use is as follows: \(\mathrm{Time\, (in\, minutes)} = \frac{\mathrm{Calories \,intake}}{\mathrm{Calories\, burned\, per\, minute}}\) Substitute the given values into the equation: \(\mathrm{Time} = \frac{120 \hspace{0.2cm}\mathrm{kcal}}{4.167 \hspace{0.2cm}\mathrm{kcal\,/ \,min}}\)

Calculate the time

Now, we can solve for the time in minutes: \(\mathrm{Time} = \frac{120}{4.167} \approx 28.8\,\mathrm{minutes}\)

Interpret the result

The result means that in order to burn the 120 kcal from a can of cola, a person needs to walk for approximately 28.8 minutes.

Key concepts

Understanding Nutritional Calories

Calories are a unit of energy measurement in nutrition. When we talk about the calories in food, we're actually referring to kilocalories (kcal), which is the amount of energy required to raise the temperature of one kilogram of water by one degree Celsius. Each food and beverage we consume has a certain number of nutritional calories, which represents the energy our bodies can get from eating or drinking it. For example, a 12-ounce can of cola typically contains about 120 kcal, which needs to be burned off through physical activities like walking to maintain energy balance.

Nutritional calories are often counted to manage weight, as consuming more than what our body expends leads to weight gain. Any exercise or physical activity helps us burn these calories and affects our energy expenditure.

Energy Expenditure Explained

Energy expenditure is the total amount of energy burned by the body to sustain basic physiological functions and physical activity. It's influenced by several factors, including age, gender, weight, height, and level of physical activity. The Total Daily Energy Expenditure (TDEE) is the sum of the Basal Metabolic Rate (BMR), which is the number of calories expended at rest, the Thermic Effect of Food (TEF), which is the energy used to digest food, and the energy used during physical activity.

Usually measured in kilocalories (kcal), understanding energy expenditure is vital for creating a balanced diet and exercise plan. For instance, activities like walking burn calories and contribute to the total energy expenditure, helping individuals maintain or lose weight as necessary.

Walking Energy Consumption

Walking is a common and effective way of burning calories. The energy consumption while walking depends on several factors such as the individual's weight, walking speed, and duration of the exercise. Generally, walking expends about 250 kcal per hour. This measure can vary; brisk walking or walking uphill, for instance, increases calorie consumption.

The beauty of using walking as an exercise is in its simplicity and accessibility. It's an aerobic activity that not only helps burn calories but also strengthens the heart, improves mood, and enhances muscular endurance. The step-by-step solution provided for the exercise demonstrates how to calculate the energy expenditure from walking, to burn off the calories from a can of cola.

Kcal to Minutes Conversion

Converting kilocalories to minutes is essential for figuring out how long you need to perform an activity to burn a specific number of calories. Knowing the rate at which an activity burns calories per minute helps in this calculation. For instance, walking burns approximately 4.167 kcal per minute (250 kcal divided by 60 minutes).

To determine the time required to burn off a particular calorie intake, we use a simple formula: Time (minutes) = Calories intake / Calories burned per minute. This formula is handy for planning workouts or daily activities to achieve calorie-burning goals, as demonstrated in the step-by-step calculation where it is used to calculate how long a person needs to walk to burn the calories from a can of cola.