Question

Jane is choosing between two exercise routines. In Routine # 1, she burns 22 calories walking. She then runs at a rate that burns 5.75 calories per minute. In Routine #2, she does only running, burning 8.5 calories per minute. For what amounts of time spent running will Routine #1 burn at least as many calories as Routine #2? Use t for the number of minutes spent running, and solve your inequality for t.​

Answer 1

Jane needs to run for 8 minutes or less in Routine #1 for it to burn at least as many calories as Routine #2. If she runs for more than 8 minutes in Routine #1, then Routine #2 will burn more calories.

Explanation:

In Routine #1, the total number of calories burned is:

C1(t) = 22 + 5.75t

The first term represents the calories burned while walking, and the second term represents the calories burned while running.

In Routine #2, the total number of calories burned is:

C2(t) = 8.5t

This represents the calories burned while running, as there is no walking in Routine #2.

We want to find the values of t for which C1(t) is greater than or equal to C2(t). So we can set up the following inequality:

C1(t) ≥ C2(t)

Substituting the expressions for C1(t) and C2(t), we get:

22 + 5.75t ≥ 8.5t

Simplifying the inequality, we get:

22 ≥ 2.75t

Dividing both sides by 2.75, we get:

t ≤ 8

So Jane needs to run for 8 minutes or less in Routine #1 for it to burn at least as many calories as Routine #2. If she runs for more than 8 minutes in Routine #1, then Routine #2 will burn more calories.

Answer 2

Answer: 3.8 minutes!

Explanation:

The answer is 3.8 minutes. To solve for t, we need to set up an inequality where the calories burned in routine #1 is equal to or greater than the calories burned in routine #2. We can write this as 22 + 5.75t ≥ 8.5t. Then, we can subtract 8.5t from both sides to get 22 ≥ -2.75t. Finally, we can divide both sides by -2.75 to get t ≤ -8/2.75, which simplifies to t ≤ 3.8. Therefore, Jane needs to run for 3.8 minutes in Routine #1 in order to burn at least as many calories as Routine #2.