How many kilocalories does a runner expend when he runs for 4.5 h and uses 710 Cal/h? How many pieces of pizza that each contain 12 g of protein, 11 g of fat, and 30 g of carbohydrates could be eaten after the race to replenish these calories?
Nutritionists years ago used cal (called small calories) and Cal (called big calories) to mean calories and kcal. If you posted the problem as is with Cal then that should mean kcal.
So you have 4.5 x 710 = about 3200 kcal used.
11 x 9 = 99 kcal
30 x 4 = 120 kcal
12 x 4 = 48 kcal
Total = 99 + 120 + 48 = 267 kcal/piece pizza.
Then ?x 267 = 3200
? pieces = 3200/267 = about 12 pieces.
That sounds about right doesn't it?
I assume Cal means kcal.
4.5 hr x (710 kcal/hr) = kcal used
11 g fat x 9 kcal = ?
30 g carb x 4 kcal = ?
12 g prot x 4 kcal = ?
Total kcal pizza per piece.
kcal/piece pizza x # pieces = kcal used.
Solve for # pieces.
Question posted was as written Cal/h.
I'm lost!!! Not sure if I'm just losing concentration after 50 chem problems or losing my mind with 3 kids running around still and a chem exam at 8am!!!
Oh ok I'm working through your answers I think I complicate the problems far beyond what I should.
To calculate the total kilocalories (kcal) the runner has expended during the race, you can multiply the running time by the calorie expenditure per hour:
Total kcal expended = Running time (h) * Calorie expenditure per hour (Cal/h)
Substituting the given values:
Total kcal expended = 4.5 h * 710 Cal/h
Multiplying 4.5 h by 710 Cal/h, we get:
Total kcal expended = 3195 kcal
Now, let's calculate the number of pieces of pizza needed to replenish these calories.
First, we need to consider the macronutrients in each piece of pizza. One piece contains:
- Protein: 12 g
- Fat: 11 g
- Carbohydrates: 30 g
The caloric value of each macronutrient per gram is as follows:
- Protein: 4 kcal/g
- Fat: 9 kcal/g
- Carbohydrates: 4 kcal/g
To calculate the total calories in each piece of pizza, we multiply the grams of each macronutrient by the respective caloric value, and then sum them up:
Total calories per piece of pizza = (Protein (g) * Caloric value of protein (kcal/g)) + (Fat (g) * Caloric value of fat (kcal/g)) + (Carbohydrates (g) * Caloric value of carbohydrates (kcal/g))
Substituting the given values and performing the calculation:
Total calories per piece of pizza = (12 g * 4 kcal/g) + (11 g * 9 kcal/g) + (30 g * 4 kcal/g)
Total calories per piece of pizza = 48 kcal + 99 kcal + 120 kcal
Total calories per piece of pizza = 267 kcal
To determine the number of pieces of pizza needed to replenish the calories expended, divide the total calories expended from running by the total calories per piece of pizza:
Number of pieces of pizza = Total kcal expended / Total calories per piece of pizza
Substituting the values:
Number of pieces of pizza = 3195 kcal / 267 kcal
Dividing 3195 kcal by 267 kcal, we get:
Number of pieces of pizza ≈ 11.97
Therefore, the runner could eat approximately 12 pieces of pizza to replenish the calories expended.