Final answer:
It would take approximately 43.7 minutes of jogging at a moderate intensity to burn off a small slice of cheesecake containing about 470 calories, given an exercise rate of 150 W and 20% efficiency. This underscores the relative ease with which one can consume more food energy than they can work off through exercise.
Step-by-step explanation:
To determine how long you would have to jog to burn off a small slice of cheesecake containing about 470 calories, we can use the information that exercising at a rate of 150 W (moderately, climbing stairs) at 20% efficiency can help us calculate the duration. First, we should convert calories to joules because energy expenditure in exercises is often measured in joules. Since 1 calorie is equivalent to 4.184 joules, we can convert 470 calories to joules:
470 kcal * 4184 J/kcal = 1966480 J
When exercising at a power output of 150 W, a person uses energy at 150 joules per second. Considering the efficiency factor of 20%, we calculate the effective power used for exercise:
150 W / 0.20 = 750 W
Now, we calculate the time needed to burn 1966480 joules at a rate of 750 joules per second:
1966480 J / 750 J/s = 2621.97 seconds
To express this time in minutes, we divide by 60, the number of seconds in a minute:
2621.97 s / 60 = 43.70 minutes
Therefore, it would take approximately 43.7 minutes of jogging at a moderate intensity with a power output of 150 W and 20% efficiency to burn off the energy from the cheesecake slice.
Implications for Weight Loss
The time it takes to burn off calories from food items like a slice of cheesecake indicates that consuming more food energy than one can reasonably expect to work off with exercise is quite easy. This points to the importance of considering both diet and exercise for effective weight management.