Alexander, who weighs 159 , decides to climb Mt. Krumpett, which is 5460 high. For his food supply, he decides to take nutrition bars. The label on the bars states that each 100- bar contains 10 of fat, 40 of protein, and 50 of carbohydrates.Alexander wants to know exactly how many bars to pack in his backpack for the journey. To provide a margin of safety, he assumes that he will need as much energy for the return trip as for the uphill climb. How many bars should Alexander pack?
How would I even go about solving this problem? The total calories is 450 for a total bar that I calculated, is this right?
Is this what they call chemistry nowadays?
How times have changed.
Is Alexander's weight in pounds? Is the moutain's height in feet?
You can compute the calorie content of the bar, but somwhere you will need an estimate of how much food energy he needs to climb the mountain and come down. It will exceed the work done, which will be less when coming down. They need to provide you with additional information. Food energy cannot be converted to work with 100% efficiency.
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Alexander, who weighs 159 , decides to climb Mt. Krumpett, which is 5460 high. For his food supply, he decides to take nutrition bars. The label on the bars states that each 100- bar contains 10 of fat, 40 of protein, and 50 of carbohydrates.Alexander wants to know exactly how many bars to pack in his backpack for the journey. To provide a margin of safety, he assumes that he will need as much energy for the return trip as for the uphill climb. How many bars should Alexander pack?
To calculate the number of bars Alexander should pack, we need to find out the total energy requirement for his journey and then determine how many bars are needed to meet that requirement.
Step 1: Calculate Alexander's total energy requirement for the entire journey.
Let's assume that Alexander's energy requirement for climbing Mt. Krumpett is proportional to his weight and the height of the mountain. We can use this proportion to calculate the energy requirement.
Energy Requirement = (Weight x Proportion) x (Mountain Height x Proportion)
In this problem, Alexander's weight is given as 159 and the mountain height is given as 5460.
Proportionally scaling the weight and height will depend on the units you choose.
For example, if you choose to scale the weight by dividing it by 100 (159/100 = 1.59) and scale the height by dividing it by 1000 (5460/1000 = 5.46), you could use the proportions 1.59 and 5.46 in the calculation.
Energy Requirement = (1.59) x (5.46)
Energy Requirement = 8.6794
Step 2: Calculate the number of calories per bar.
You mentioned that each bar contains 10 grams of fat, 40 grams of protein, and 50 grams of carbohydrates. We can use the following conversion rates to calculate the number of calories per bar:
1 gram of fat = 9 calories
1 gram of protein = 4 calories
1 gram of carbohydrates = 4 calories
Now let's calculate the calories per bar:
Calories per bar = (10 x 9) + (40 x 4) + (50 x 4)
Calories per bar = 90 + 160 + 200
Calories per bar = 450
Step 3: Calculate the number of bars needed.
To find the number of bars needed, divide the total energy requirement by the calories per bar:
Number of bars needed = Energy Requirement / Calories per bar
Number of bars needed = 8.6794 / 450
Number of bars needed ≈ 0.0193 (approximately)
Since you cannot pack a fractional number of bars, you would round up to the nearest whole number, which means Alexander should pack at least 1 bar for his journey.
However, since Alexander assumes that he will need as much energy for the return trip, it would be prudent to double the number of bars. So, he should pack 2 bars in his backpack for the journey.
Please note that the scaling proportion and rounding may vary depending on the context and preferences, but the steps provided above outline a general approach to solving the problem.