Step-by-step explanation:
To determine the number of minutes it would take to burn off the slice of cake, we need to calculate the total energy content of the cake slice and then divide it by the rate at which swimming burns energy.
First, let's calculate the energy content of the cake slice. We have the following information:
- Fat: 29.0 grams with a fuel value of 38 kJ/g.
- Protein: 9.0 grams with a fuel value of 17 kJ/g.
- Carbohydrate: 77 grams with a fuel value of 17 kJ/g.
Calculating the energy content for each component:
- Fat: 29.0 grams * 38 kJ/g = 1,102 kJ
- Protein: 9.0 grams * 17 kJ/g = 153 kJ
- Carbohydrate: 77 grams * 17 kJ/g = 1,309 kJ
Now, we can find the total energy content of the cake slice:
Total energy content = Fat energy + Protein energy + Carbohydrate energy
Total energy content = 1,102 kJ + 153 kJ + 1,309 kJ = 2,564 kJ
Next, we need to determine how many minutes it would take to burn off 2,564 kJ of energy. We know that swimming burns energy at a rate of 1,000 kJ/hour. To convert this to minutes, we divide by 60 (minutes in an hour):
Energy burned per minute = 1,000 kJ/hour / 60 minutes/hour = 16.67 kJ/minute
Finally, we divide the total energy content of the cake slice by the energy burned per minute:
Time (in minutes) = Total energy content / Energy burned per minute
Time (in minutes) = 2,564 kJ / 16.67 kJ/minute ≈ 154 minutes
Therefore, it would take approximately 154 minutes to completely burn off the slice of cake.
The closest option to this value is (d) 154.