The problem asks us to draw a distance-time graph of Katie's journey to the beach and back home. She leaves home at 11:00, arrives at the beach (30 miles away) at 12:00, stays there until 14:00, and then returns home, arriving at 14:30.

1. Problem Description

The problem asks us to draw a distance-time graph of Katie's journey to the beach and back home. She leaves home at 11:00, arrives at the beach (30 miles away) at 12:00, stays there until 14:00, and then returns home, arriving at 14:

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2. Solution Steps

* From 11:00 to 12:00, Katie travels from home (0 miles) to the beach (30 miles). We plot the points (11:00, 0) and (12:00, 30) and draw a straight line between them to represent the constant speed.

* From 12:00 to 14:00, Katie stays at the beach, so her distance from home remains constant at 30 miles. We plot the point (14:00, 30) and draw a horizontal line from (12:00, 30) to (14:00, 30).

* From 14:00 to 14:30, Katie travels from the beach (30 miles) back home (0 miles). We plot the point (14:30, 0) and draw a straight line from (14:00, 30) to (14:30, 0) to represent her constant speed.

3. Final Answer

The distance-time graph consists of three line segments:

* A line segment from (11:00, 0) to (12:00, 30).

* A horizontal line segment from (12:00, 30) to (14:00, 30).

* A line segment from (14:00, 30) to (14:30, 0).

Since this response is text-only, I am unable to visually reproduce the graph. But by following the steps above and plotting the described line segments on the given axes, you will have the correct distance-time graph of Katie's journey.