This is not a homework question because I have completed my school/college. I am posting this question here because somebody asked me and it confuses me. So I want to know (as soon as I can) how to solve it.

Each pound of fat contains 3500 food calories. When the body metabolizes food, 80.0 % of this energy goes to heat. Suppose you decide to run without stopping, an activity that produces 1290 W of metabolic power for a typical person.
For how many hours must you run to burn up 1.00 lb of fat?

Now, let me explain what confuses me in this question. I solved it as follows:-

Total energy in 1 lb of fat = 3500 food calories = 3500 * 1000 cal = 3500 * 1000 * 4.18 J = 1.463 * 10^7 J
Metabolic energy E = 20% of 1.463 * 10^7 J = 1.463 * 10^7 * 20/100 = 2.926 * 10^6 J
Metabolic power P = 1290 W
Time t = E/P = 2.926 * 10^6/1290 = 2268.217 sec = 2268.217/3600 hour = 0.63 hour
Ans: 0.63 hour

But this answer is wrong. I thought that 80% is lost into heat. So 20% should be metabolic energy. But that seems to be wrong.
So let me know what I am doing wrong.

Where did you get the figure of 1290 watts of "metabolic power" for a typical person? That sounds like a lot, especially if this person has to produce this much power continuously during exercise. Given your figure of 20% efficiency of the person's muscles, this means the person is producing heat at a rate of 1290*4 = 5160 watts! I sincerely doubt that this is possible.

Given the numbers you state, the math looks right, but I would check that power figure.