Miguel is choosing between two exercise routines.
In Routine #1, he does only running, burning 15 calories per minute.
In Routine #2, he burns 12 calories walking. He then runs at a rate that burns 12 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.
While hiking, Mr. Finds burns 808 Calories in 8 hours. At this rate, how many Calories does he burn in 60 minutes?
Let's solve the problem step by step:
Step 1: Determine the number of calories burned in Routine #1 and #2
In Routine #1, the number of calories burned per minute is 15.
In Routine #2, the number of calories burned walking is 12 and running is also 12 calories per minute.
Step 2: Set up the inequality to compare the number of calories burned in each routine
We want to find the amount of time spent running in Routine #2 (t) that will make Routine #1 burn more calories than Routine #2. Since Routine #1 burns more calories, we can set up the following inequality:
15t > 12(12 + t)
Step 3: Solve the inequality
Let's solve for t:
15t > 12(12 + t)
15t > 144 + 12t
15t - 12t > 144
3t > 144
t > 144/3
t > 48
Step 4: Interpret the solution
The solution to the inequality is t > 48. This means that Routine #1 will burn more calories than Routine #2 when Miguel spends more than 48 minutes running in Routine #2.
Therefore, for amounts of time spent running greater than 48 minutes, Routine #1 will burn more calories than Routine #2.
To determine for what amounts of time spent running Routine #1 will burn more calories than Routine #2, we need to set up an inequality.
Let's assume that Miguel spends t minutes running in both routines.
In Routine #1, the number of calories burned is given by:
Calories burned in Routine #1 = 15 * t
In Routine #2, the number of calories burned is given by:
Calories burned walking in Routine #2 = 12 * (60 - t)
Calories burned running in Routine #2 = 12 * t
The total number of calories burned in Routine #2 is the sum of the calories burned walking and the calories burned running:
Total calories burned in Routine #2 = Calories burned walking in Routine #2 + Calories burned running in Routine #2
Total calories burned in Routine #2 = 12 * (60 - t) + 12 * t
To find when Routine #1 burns more calories than Routine #2, we need to set up the inequality:
Calories burned in Routine #1 > Total calories burned in Routine #2
Substituting the given expressions:
15 * t > 12 * (60 - t) + 12 * t
Now, let's solve this inequality for t:
15t > 720 - 12t + 12t
15t > 720
t > 720 / 15
t > 48
So, for t > 48 minutes, Routine #1 will burn more calories than Routine #2.
Note: Since it's not possible to have fractional minutes of exercise, the answer is t > 48. This means that Miguel would need to spend more than 48 minutes running in Routine #1 for it to burn more calories than Routine #2.
routine #1:
Amt = 15t
routine #2 = 12 + 12t
when is
15t > 12+12t
easy to solve