How many food calories can a human burn up in an hour by exercising at this rate? (remember that only 20.0 % of the food energy used goes into mechanical energy.) ?

Human can produce a maximum mechanical power of 1/3 hp (horse-power).

Horse power is a unit of power, it equals 746 watt (watt is also a power unit, known to be equal to a joule per second)

So:

1 ph = 746 watt = 746 J/s

1/3 ph = 248.6 J/s

we're looking for the calories, so

1 joule = 0.239006 calories

So human produce a maximum mechanical power of:

248.6 J/s = 82.88 calories per second.

We're looking for the number of calories consumed in three hours, so:

82.88 cal/s = 82.88 cal/s * 3600 s * 3 = 895200 calories = 895.2 kilocalories (food calories).

The number of food calories is 895.2 food calories