The graph represents Aidan's walking trip to his friend’s house, and we are tasked with finding the value of $d$, which represents the distance from Aidan's home to his friend’s house.

Key observations from the graph:

• Aidan walked from home to his friend's house in 15 minutes.
• He stayed at his friend’s house for 30 minutes.
• He walked back home in 10 minutes.
• The total distance he walked to his friend's house is 900 meters (as given in the text).

Step-by-step breakdown:

1. Slope of the first segment (walking to his friend’s house):

   • Aidan covered 900 meters in 15 minutes. Thus, the slope or speed during this segment can be calculated as: $\text{Speed} = \frac{900 \, \text{m}}{15 \, \text{minutes}} = 60 \, \text{meters per minute}$

2. Plateau segment (staying at his friend’s house):

   • For the 30-minute period from 15 minutes to 45 minutes, Aidan stayed at his friend’s house, meaning he didn't change distance during this time. This is represented by the flat line on the graph.

3. Slope of the final segment (walking back home):

   • Aidan walked back home in 10 minutes, covering the same 900 meters. His speed on the return trip was: $\text{Speed} = \frac{900 \, \text{m}}{10 \, \text{minutes}} = 90 \, \text{meters per minute}$

Thus, the distance $d$ is equal to 900 meters, as this represents the total distance Aidan traveled away from his home.

Final Answer:

$d = 900 \, \text{meters}$

Would you like more details or have any further questions?

Here are 5 related questions:

1. What is the total distance Aidan walked during his trip?
2. How would the graph change if Aidan walked to a different location 1200 meters away?
3. How can you calculate the total time Aidan spent on his journey, including the stop at his friend's house?
4. What is the average speed of Aidan for the entire journey?
5. How does the slope of a line on a distance-time graph relate to speed?

Tip: On a distance-time graph, a steeper slope indicates a higher speed, and a horizontal line means the object is stationary.