Question

heather is choosing between two exercise routines.
in routine #1, she does only running, burning 15.5 calories per minute.
in routine #2, she burns 26 calories walking. she then runs at a rate that burns 12.9 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.

Explanation:

Step1: Define Calories for Each Routine

Routine #1: Calories = \( 15.5t \) (15.5 per min, \( t \) mins).
Routine #2: Calories = \( 26 + 12.9t \) (26 walking + 12.9 per min running).

Step2: Set Up Inequality

Routine #1 ≥ Routine #2:
\( 15.5t \geq 26 + 12.9t \)

Step3: Solve for \( t \)

Subtract \( 12.9t \) from both sides:
\( 15.5t - 12.9t \geq 26 \)
\( 2.6t \geq 26 \)

Divide by 2.6:
\( t \geq \frac{26}{2.6} \)
\( t \geq 10 \)

Answer:

\( t \geq 10 \) (Heather needs to run at least 10 minutes in Routine #1.)