At a speed of 45 yards per minute, a 120 pound swimmer burns 600 calories per hour. Use two different methods to write a linear equation that models the number of calories burned per hour as a function of a swimmer's weight
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To write a linear equation that models the number of calories burned per hour as a function of a swimmer's weight, we need to understand the relationship between weight and calories burned.
Method 1: Using the given information:
We are given that a 120 pound swimmer burns 600 calories per hour. Let's assume this serves as our baseline and acts as a starting point for calculating the linear equation.
1 pound is equivalent to approximately 0.45 kilograms. To convert pounds to kilograms, we can multiply the weight in pounds by 0.45. Therefore, the weight of the swimmer in kilograms would be 120 * 0.45 = 54 kilograms.
We know that the rate of calories burned is proportional to the speed. In this case, the speed is given as 45 yards per minute. To convert yards per minute to meters per minute, we can multiply by a conversion factor. 1 yard is approximately equal to 0.9144 meters. Hence, the speed in meters per minute would be 45 * 0.9144 = 41.144 meters per minute.
Next, we can calculate the calories burned per minute for the 120-pound swimmer. Since the speed is given in yards per minute, we will use the conversion: 1 yard is approximately equal to 0.9144 meters. Therefore, 45 yards per minute is equal to 41.144 meters per minute. Multiplying this speed by the weight in kilograms, we get 41.144 * 54 = 2224.176 calories.
Since there are 60 minutes in an hour, the number of calories burned per hour for the 120-pound swimmer would be 2224.176 * 60 = 133450.56 calories.
Now, let's use this information to write the linear equation:
Let x represent the weight of the swimmer in pounds, and y represent the number of calories burned per hour.
We can set up a proportion between the weight and calories burned per hour:
120 pounds / 133450.56 calories = x pounds / y calories.
To find the linear equation, we can cross-multiply:
120y = 133450.56x.
Divide both sides of the equation by 120:
y = (133450.56 / 120)x.
Simplifying the equation gives us:
y = 1112.88x.
So, the linear equation is y = 1112.88x, where y represents the number of calories burned per hour, and x represents the weight of the swimmer in pounds.
Method 2: Using the formula for calculating calories burned:
Another method to derive the linear equation is by using the formula for calculating calories burned, which is:
calories burned = weight (in kg) * duration (in hours) * metabolic equivalent (MET).
The MET value depends on the activity being performed. In this case, swimming has an MET value of 7.5.
Therefore, the linear equation for the number of calories burned per hour as a function of a swimmer's weight can be written as:
y = 7.5 * x,
where y represents the number of calories burned per hour, and x represents the weight of the swimmer in pounds.