To determine the average speed for the given graph of distance (in km) over time, we can break the journey into two parts: from home to a friend's house, and then from the friend's house to school.

Step-by-step analysis:

1. From Home to Friend's House:

   • The first segment of the graph shows the distance increasing from 0 km to approximately 1 km between 0 to 20 minutes.
   • The formula for speed is: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
     • Distance: 1 km
     • Time: 20 minutes (or 1/3 hours)
     • Speed for this segment: $\text{Speed} = \frac{1 \text{ km}}{\frac{1}{3} \text{ hours}} = 3 \text{ km/h}$

2. From Friend's House to School:

   • The second segment shows an increase from 1 km to 3 km, taking 40 minutes (from 20 to 60 minutes).
   • Distance: 2 km (from 1 km to 3 km)
   • Time: 40 minutes (or 2/3 hours)
   • Speed for this segment: $\text{Speed} = \frac{2 \text{ km}}{\frac{2}{3} \text{ hours}} = 3 \text{ km/h}$

Overall Average Speed:

The total distance is 3 km, and the total time taken is 1 hour (60 minutes). Therefore, the average speed for the entire journey is: $\text{Average Speed} = \frac{3 \text{ km}}{1 \text{ hour}} = 3 \text{ km/h}$

So, the average speed for the entire journey is 3 km/h.

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Related questions:

1. What is the difference between instantaneous speed and average speed?
2. How does the slope of a distance-time graph relate to speed?
3. If she had walked at a constant speed, would her average speed change?
4. How can we determine the time spent at her friend's house if it was a rest stop?
5. What would happen to the average speed if she slowed down between her friend's house and school?

Tip: On a distance-time graph, a steeper slope indicates a higher speed!