Jose is choosing between two exercise routines.
In Routine #1, he burns 17 calories walking. He then runs at a rate that burns 4.25 calories per minute.
In Routine #2, he does only running, burning 8.5 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 t.
Let's set up the inequality to represent the problem:
17 + 4.25t > 8.5t
Simplifying the inequality:
17 > 8.5t - 4.25t
17 > 4.25t
To isolate t, divide both sides of the inequality by 4.25:
4 > t
The inequality is now:
t < 4
Therefore, for any amount of time spent running (t) less than 4 minutes, Routine #1 will burn more calories than Routine #2.
To compare the calorie burn of Routine #1 and Routine #2, let's calculate the total calories burned for each routine based on the time spent running.
In Routine #1:
Calories burned from walking = 17 calories
Calories burned from running = 4.25 calories/minute * t minutes
Total calories burned in Routine #1 = Calories burned from walking + Calories burned from running
= 17 + (4.25 * t)
In Routine #2:
Calories burned from running = 8.5 calories/minute * t minutes
Total calories burned in Routine #2 = Calories burned from running
= 8.5 * t
To find the time (t) for which Routine #1 burns more calories than Routine #2, we set up the inequality:
Total calories burned in Routine #1 > Total calories burned in Routine #2
17 + (4.25 * t) > 8.5 * t
To solve this inequality for t, follow these steps:
1. Subtract 4.25 * t from both sides of the inequality:
17 > 8.5 * t - 4.25 * t
2. Combine like terms on the right side of the inequality:
17 > 4.25 * t
3. Divide both sides of the inequality by 4.25:
4 > t
Therefore, when the time spent running (t) is less than 4 minutes, Routine #1 will burn more calories than Routine #2.
To find the amount of time spent running in Routine #1 that will burn more calories than Routine #2, we can set up an inequality.
Let t be the number of minutes spent running in Routine #1.
In Routine #1, the total number of calories burned can be calculated as follows:
Calories burned in walking = 17 calories
Calories burned in running = 4.25 calories/minute * t minutes
Total calories burned in Routine #1 = 17 calories + 4.25 calories/minute * t minutes
In Routine #2, the total number of calories burned can be calculated as follows:
Calories burned in running = 8.5 calories/minute * t minutes
Now, we want to find the values of t for which the total calories burned in Routine #1 is greater than the total calories burned in Routine #2. This can be represented as an inequality:
17 calories + 4.25 calories/minute * t minutes > 8.5 calories/minute * t minutes
Simplifying the inequality:
17 + 4.25t > 8.5t
To isolate t, we can subtract 4.25t from both sides:
17 > 8.5t - 4.25t
Combining like terms:
17 > 4.25t
To solve for t, we divide both sides by 4.25:
17/4.25 > t
4 > t
Therefore, for any value of t greater than 4, Routine #1 will burn more calories than Routine #2.
In summary, if Jose spends more than 4 minutes running in Routine #1, it will burn more calories than Routine #2.