please help
Ahmad is choosing between two exercise routines.
In Routine #1, he burns 22 calories walking. He then runs at a rate that burns 15.5 calories per minute.
In Routine #2, he burns 48 calories walking. He then runs at a rate that burns 10.3 calories per minute.
For what amounts of time spent running will Routine #1 burn fewer calories than Routine #2?
Use t for the number of minutes spent running, and solve your inequality for t.
22 + 15.5t < 48 + 10.3t
Solve for t.
To find the amount of time spent running where Routine #1 burns fewer calories than Routine #2, we need to set up an inequality.
First, let's calculate the total calories burned for each routine:
For Routine #1:
Calories burned walking = 22
Calories burned running = 15.5t (where t is the number of minutes spent running)
Total calories burned in Routine #1 = 22 + 15.5t
For Routine #2:
Calories burned walking = 48
Calories burned running = 10.3t (where t is the number of minutes spent running)
Total calories burned in Routine #2 = 48 + 10.3t
To find when Routine #1 burns fewer calories than Routine #2, we set up the inequality:
22 + 15.5t < 48 + 10.3t
Now we can solve this inequality for t:
22 + 15.5t - 10.3t < 48
Simplifying the inequality, we get:
5.2t < 48 - 22
5.2t < 26
Divide both sides of the inequality by 5.2:
t < 26 / 5.2
t < 5
Therefore, if Ahmad spends fewer than 5 minutes running, Routine #1 will burn fewer calories than Routine #2.
To find the time spent running at which Routine #1 burns fewer calories than Routine #2, we need to compare the total calories burned in each routine.
In Routine #1, the total calories burned can be calculated as follows:
Calories burned walking = 22
Calories burned running = 15.5t (where t is the number of minutes spent running)
Total calories burned = Calories burned walking + Calories burned running = 22 + 15.5t = 15.5t + 22
In Routine #2, the total calories burned can be calculated as follows:
Calories burned walking = 48
Calories burned running = 10.3t (where t is the number of minutes spent running)
Total calories burned = Calories burned walking + Calories burned running = 48 + 10.3t = 10.3t + 48
We want to find the values of t for which Routine #1 burns fewer calories than Routine #2, so we set up an inequality:
15.5t + 22 < 10.3t + 48
Now, let's solve this inequality for t:
15.5t - 10.3t < 48 - 22
5.2t < 26
t < 26/5.2
t < 5
Therefore, for any value of t less than 5 minutes, Routine #1 will burn fewer calories than Routine #2.