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.
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.
From your data, all I get is:
15t > 12t, which applies for all values of t.
10 cals per min A
20 cals per min B
30 cals per min C
50 cals per min D
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.