A 25-year old woman burns 300 - 80 t 300-80t cal/hr while walking on her treadmill. Her caloric intake from drinking Gatorade is 50 t 50t calories during the t tth hour. What is her net decrease in calories after walking for 3 hours?

The net decrease in calories after walking 3 hours is 210 cal (if the Gatorade intake is discrete) or 765 cal (if the Gatorade intake is continuous)

Explanation:

The net decrease N in calories after 3 hours will be

N=Net decrease = Decrease due to walking - Increase because of Gatorade

= 300 - 80*t + 50*t = 300 - 30*t

- if the Gatorade intake is discrete (1 gatorade each hour with 30 calories intake, so there is total intake of 30*t at time t), then for t = 3 hours

Net decrease = 300 cal - 30 cal/hour * 3 hours = 300 cal - 90 cal = 210 cal

Net decrease = 210 cal

- if the Gatorade intake is continuous (continuously drinking Gatorade during the walk), then

N = ∫ (300 - 30*t) dt = 300*t - 30*t²/2 (integrated between t and t=0)

then for t=3 hours

N = 300*3 - 30*3²/2 = 765 cal