Alexander, who weighs 174lb , decides to climb Mt. Krumpett, which is 5810m high

Question

Alexander, who weighs 174lb , decides to climb Mt. Krumpett, which is 5810m high. For his food supply, he decides to take nutrition bars. The label on the bars states that each 100-g bar contains 10g of fat, 40 g of protein, and 50 g of carbohydrates.

One gram of fat contains 9 Calories, whereas each gram of protein and carbohydrates contains 4 Calories.

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?

I calculated 4.4 bars but it said i was wrong>>>> thanks for the help

Explanation / Answer

Let us calculate the amount of energy requried to climb

E=mgh
174 is 79.1kg on earth.

E=(79.1kg)(9.8m/s^2)(5810m) = 4503795.8 Joules.

Times 2 for the way down =9007591.6 Joules

We need to convert joules into Calories

1J = 0.239cal

9007591.6 Joules is 2.152 X10^3 kcal.

Now lets calculate the amount of energy per bar.
Protein and carbohydrates are 4cal per gram, fat is 9cal per gram

so calories from each bar is equal to

10g X9cal/g +40g X4cal/g + 50g X 4kcal/g = 450 cal per bar.

so bars needed = total energy required / calories from each bar = 2.152 X10^6 cal. / 450 cal = 4782.22 bars

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