Observe the graph:

One reason for the variation in average rate of change may be that Simeons family encountered traffic later in their trip, thus slowing them down. 

Another may be that Simeones family travelled on residential roads for the first hour before entering a highway for the next three hours.

The two instance on the graph where Simeons family appeares to not travel any distance may be as a result of the family needing to stop to eat or take a break.

They may have also encountered an accident where traffic was completely stopped.

One reason for the variation in average rate of change may be that Simeons family encountered traffic later in their trip, thus slowing them down.

Another may be that Simeons family travelled on residential roads for the first hour before entering a highway for the next three hours.

The two instance on the graph where Simeons family appeares to not travel any distance may be as a result of the family needing to stop to eat or take a break.

They may have also encountered an accident where traffic was completely stopped.