The problem describes Vanessa's journey, which involves cycling and resting. We need to draw a distance-time graph to represent her journey, given that she cycled 20 km in 30 minutes, rested for 15 minutes, and then cycled another 10 km in 45 minutes.

1. Problem Description

The problem describes Vanessa's journey, which involves cycling and resting. We need to draw a distance-time graph to represent her journey, given that she cycled 20 km in 30 minutes, rested for 15 minutes, and then cycled another 10 km in 45 minutes.

2. Solution Steps

Step 1: Plot the first cycling segment.

Vanessa cycled 20 km in 30 minutes. This gives us the point (30, 20) on the graph. Since she started at home, the journey starts at (0, 0). Draw a straight line from (0, 0) to (30, 20).

Step 2: Plot the resting segment.

Vanessa rested for 15 minutes. During this time, her distance remains constant. So, from 30 minutes to 30 + 15 = 45 minutes, her distance is 20 km. This gives us the point (45, 20). Draw a horizontal line from (30, 20) to (45, 20).

Step 3: Plot the second cycling segment.

Vanessa cycled another 10 km in 45 minutes. So, after 45 minutes + 45 minutes = 90 minutes, her total distance is 20 km + 10 km = 30 km. This gives us the point (90, 30). Draw a straight line from (45, 20) to (90, 30).

3. Final Answer

The distance-time graph of Vanessa's journey consists of:

- A straight line from (0, 0) to (30, 20)

- A horizontal line from (30, 20) to (45, 20)

- A straight line from (45, 20) to (90, 30)

(Note: Since this is a text-based response, I cannot draw the graph. The description above details how to draw the graph on the provided axes.)