Linear Equation

Sample Solution

Swimming laps for calorie burn and food intake

Swimming is a great exercise for burning calories, offering various intensities depending on swimming style and effort. Let's create a linear model to represent the relationship between calories burned and the number of laps swum, keeping in mind daily food intake variations.

Scenario:

Consider an individual swimming at a moderate pace, burning approximately 70 calories per 20 laps. We'll model calorie burn (C) for a given number of laps swum (L) while accounting for daily food intake (I) ranging from 1800 to 2500 calories.

Linear Model:

Full Answer Section

C = 0.7L - I

• C represents the number of calories burned (dependent variable).
• L represents the number of laps swum (independent variable).
• I represents the daily food intake in calories.

Example Questions:

1. How many calories are burned after a typical session of 40 laps?

Using the formula, we plug in L = 40:

C = (0.7 * 40) - I

Since we don't have a specific food intake (I) value, we cannot calculate the exact calorie burn. However, we can provide a range based on the given intake range:

• For I = 1800: C = (0.7 * 40) - 1800 = 8 calories burned.
• For I = 2500: C = (0.7 * 40) - 2500 = -1640 calories burned (impossible, as you cannot burn more than consumed).

2. How many laps do I need to swim to burn all the calories eaten in a day?

Again, we need the specific food intake (I) to solve:

L = (I + C) / 0.7

Assuming an average intake of 2150 calories and aiming for complete calorie burn (C = 0):

L = (2150 + 0) / 0.7 ≈ 3071.43 laps

This implies swimming approximately 3071 laps, which might be unrealistic in a single session. Remember, this is a simplified model, and factors like individual metabolism and swimming intensity can affect actual calorie burn.

Discussion:

Feel free to analyze this model and answer the following questions:

• Does the chosen calorie burn rate per lap seem reasonable? What factors could affect this rate?
• How would you modify the model to account for different swimming intensities or activities?
• Are there any limitations to using a linear equation for this scenario?
• What additional information would be helpful to create a more accurate model?

By discussing these questions, we can gain a deeper understanding of linear models and their applications in real-life scenarios.