Question 10 $0 / 2$ pts 100 $\rightleftarrows 9$ A 25-year old woman burns $350-60 t \mathrm{cal} / \mathrm{hr}$ while walking on her treadmill. Her caloric intake from drinking Gatorade is $80 t$ calories during the $t$ th hour. What is her net decrease in calories after walking for 3 hours? calories burned Question Help: $\square$ Message instructor Submit Question Jump to Answer

Step 1 ：The problem states that a 25-year old woman burns $350-60t$ calories per hour while walking on her treadmill. Her caloric intake from drinking Gatorade is $80t$ calories during the $t$ th hour. We are asked to find her net decrease in calories after walking for 3 hours.

Step 2 ：The net decrease in calories is the difference between the calories burned and the calories consumed. The calories burned is given by the function $350-60t$ and the calories consumed is given by the function $80t$.

Step 3 ：We need to integrate these functions over the interval from 0 to 3 hours to find the total calories burned and consumed. The total calories burned is $780$ and the total calories consumed is $360$.

Step 4 ：Subtract the total calories consumed from the total calories burned to find the net decrease. The net decrease in calories is $780 - 360 = 420$.

Step 5 ：Final Answer: The net decrease in calories after walking for 3 hours is \(\boxed{420}\).