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.
It would help if you proofread your questions before you posted them.
From your data, all I get is:
15t > 12t, which applies for all values of t.
During 30 minutes on the treadmill, Latoya burned 20 calories per minute. What is the rate of change of the function that represents this situation?
50
During 30 minutes on the treadmill, LaToya burned 20 calories per minute. What is the rate of change of the function that represents this situation?
10 cals per min A
20 cals per min B
30 cals per min C
50 cals per min D
To compare the caloric burn of Routine #1 and Routine #2, we need to set up an inequality based on the number of minutes spent running. Let's break it down step by step:
In Routine #1, the number of calories burned is given by 15t, where t represents the time spent running in minutes.
In Routine #2, the number of calories burned while walking is 12 times the total time spent. After that, the number of calories burned while running is also 12t.
To find when Routine #1 burns more calories than Routine #2, we need to set up the inequality:
15t > (12 * t + 12t)
Simplifying this inequality gives:
15t > 12t + 12t
15t > 24t
Now, we can solve for t:
15t - 24t > 0
-9t > 0
t < 0
The result tells us that the routine burns more calories when t is negative, which doesn't make sense in this context. Therefore, there is no amount of time spent running where Routine #1 burns more calories than Routine #2.