Dale is choosing between two exercise routines. In Routine #1, he does only running, burning 10 calories per minute. In Routine #2, he burns 10 calories walking. He then runs at a rate that burns 8 calories per minute. For what amounts of time spent running will Routine #1 burn more calories than Routine #2? Use for the number of minutes spent running, and solve your inequality for .
To compare the number of calories burned in each routine, we need to set up an inequality. Let's assume Dale spends "x" minutes running in Routine #1.
In Routine #1, Dale burns 10 calories per minute running. Therefore, in "x" minutes, he will burn a total of 10x calories.
In Routine #2, Dale burns 10 calories walking and 8 calories per minute running. Since he needs to walk before he starts running, he has (x + 1) minutes where he burns 10 calories walking and (x) minutes where he burns 8x calories running. The total number of calories burned in Routine #2 is: 10 + 8x.
Now, we can set up the inequality to solve for x:
10x > 10 + 8x
Subtracting 8x from both sides, we have:
2x > 10
Dividing both sides by 2, we find:
x > 5
Therefore, for any amount of time spent running (x) greater than 5 minutes, Routine #1 will burn more calories than Routine #2.
Thus, the solution to the inequality is x > 5.