Question

Isabel is choosing between two exercise routines. In Routine #1, she does only running, burning 10.5 calories per minute. In Routine #2, she burns 19 calories walking and then runs at a rate that burns 5.75 calories per minute. For what amounts of time spent running will Routine #1 burn more calories than Routine #2?

A. t > 9.3 minutes
B. t < 9.3 minutes
C. t = 9.3 minutes
D. t ≤ 9.3 minutes

Answer 1

To determine the amounts of time spent running that will result in Routine #1 burning more calories than Routine #2, set up and solve an equation. Routine #1 will burn more calories than Routine #2 for t > 4 minutes.

Step-by-step explanation:

To determine the amounts of time spent running that will result in Routine #1 burning more calories than Routine #2, we need to set up an equation and solve for the time. Let's assume that Isabel spends t minutes running in Routine #2.

In Routine #1, Isabel only runs, burning 10.5 calories per minute. Therefore, the total calories burned in Routine #1 can be calculated as 10.5t.

In Routine #2, Isabel burns 19 calories walking and then runs for t minutes at a rate of 5.75 calories per minute. The total calories burned in Routine #2 can be calculated as 19 + 5.75t.

Now, we need to find the values of t for which Routine #1 burns more calories than Routine #2. This can be represented mathematically as:

10.5t > 19 + 5.75t

Simplifying the equation, we get:

4.75t > 19

Dividing both sides of the equation by 4.75, we find:

t > 19/4.75

t > 4

Hence, Routine #1 will burn more calories than Routine #2 for t > 4 minutes.