David is choosing between two exercise routines.
In Routine #1, he burns 18 calories walking. He then runs at a rate that burns 10.25 calories per minute.
In Routine #2, he does only running, burning 12.5 calories per minute.
For what amounts of time spent running will Routine #1 burn more calories than Routine #2?
Use t for the number of minutes spent running, and solve your inequality for t.
Tell you what. I'll build the inequality, and you solve it ...
18 + 10.25t > 12.5t
To find the amount of time spent running where Routine #1 burns more calories than Routine #2, we need to set up an inequality.
Let's calculate the total number of calories burned for each routine based on the time spent running.
In Routine #1, David burns 18 calories walking and then an additional 10.25 calories per minute running. So the total calories burned in Routine #1 is given by: 18 + 10.25t, where t is the number of minutes spent running.
In Routine #2, David only does running and burns 12.5 calories per minute. So the total calories burned in Routine #2 is given by: 12.5t.
Now, we want to find the values of t for which Routine #1 burns more calories than Routine #2. Mathematically, this can be expressed as:
18 + 10.25t > 12.5t
To solve this inequality for t, we will isolate the variables on one side:
18 > 12.5t - 10.25t
18 > 2.25t
Dividing both sides of the inequality by 2.25, we get:
(18 / 2.25) > t
8 > t
Therefore, Routine #1 will burn more calories than Routine #2 for any values of t less than 8.
In conclusion, if David spends less than 8 minutes running, Routine #1 will burn more calories compared to Routine #2.
To determine when Routine #1 burns more calories than Routine #2, we need to set up an inequality equation.
Let's calculate the total calories burned for each routine.
In Routine #1:
Calories burned from walking = 18
Calories burned from running = 10.25t
Total calories burned in Routine #1 = 18 + 10.25t
In Routine #2:
Calories burned from running = 12.5t
Now, we can set up the inequality equation:
18 + 10.25t > 12.5t
To solve this inequality for t, we can solve it step-by-step.
Step 1:
18 + 10.25t > 12.5t
Step 2:
18 > 12.5t - 10.25t
Step 3:
18 > 2.25t
Step 4:
18 / 2.25 > t
Step 5:
8 > t
Therefore, for any value of t less than 8 minutes, Routine #1 will burn more calories than Routine #2.