Question

d. where was isaac 3 hours after school ended?

1. lexie completed an 18-mile triathlon. she swam 1 mile in 1 hour, 12 miles in 1 hour, and then ran 5 miles in 1 hour.

$l(t) = \

$$\begin{cases} t, & 0 \\leq t \\leq 1 \\\\ 12t - 11, & 1 < t \\leq 2 \\\\ 5t + 3, & 2 < t \\leq 3 \\end{cases}$$

$
a. create the graph of the piecewise function $l(t)$.
graph of a function on a grid is shown here

Explanation:

To determine where Isaac was 3 hours after school ended, we analyze the piecewise function \( L(t) \) for \( t = 3 \).

Step 1: Identify the relevant piece of the function

The function \( L(t) \) is defined as:
\[
L(t) =

$$\begin{cases} t, & 0 \leq t \leq 1 \\ 12t - 11, & 1 < t \leq 2 \\ 5t + 3, & 2 < t \leq 3 \end{cases}$$

\]
For \( t = 3 \), we use the third piece: \( 5t + 3 \) (since \( 2 < 3 \leq 3 \)).

Step 2: Substitute \( t = 3 \) into the third piece

Substitute \( t = 3 \) into \( 5t + 3 \):
\[
L(3) = 5(3) + 3
\]

Step 3: Calculate the result

Simplify the expression:
\[
L(3) = 15 + 3 = 18
\]

Thus, 3 hours after school ended, Isaac was at 18 miles (the end of the triathlon).

Answer:

Isaac was 18 miles from the starting point (or at the end of the triathlon) 3 hours after school ended.