Question

jose is choosing between two exercise routines. in routine #1 he burns 44 calories walking. he then runs at a rate that burns 12.75 calories per minute. in routine #2 he burns 22 calories walking. he then runs at a rate that burns 15.5 calories per minute.for what amount of time spent running will routine #1 burn fewer calories than routine #2.use t for the number of minutes spent running and solve your inequality for t.

Answer 1

Greater than 8 minutes

Step-by-step explanation:

Let the number of minutes spent running = t

Routine 1

Number of calories burnt walking = 44

Rate of burning calories when running = 12.75 calories per minute.

`\begin{gathered} 12.75=\frac{Number\text{ of calories}}{t} \\ Number\text{ of calories}=12.75t \end{gathered}`

Total calories burnt in Routine 1 = 44+12.75t

Routine 2

Number of calories burnt walking = 22

Rate of burning calories when running = 15.5 calories per minute.

Total calories burnt in Routine 2 = 22+15.5t

Therefore, when routine #1 burn fewer calories than routine #2, we have:

`44+12.75t<22+15.5t`

We then solve for t.

[tex]\begin{gathered} 44-22<15.5t-12.75t \\ 22<2.75t \\ \frac{22}{2.75}<\frac{2.75t}{2.75} \\ 8When the amount of time is greater than 8 minutes, routine #1 will burn fewer calories than routine #2.