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In this problem, Aly throws a stick, and the dog runs to collect it and return to Aly, while Aly walks slowly towards the dog. We need to find which graph best represents the distance between Aly and the dog over time.

1. **Graph A**: 
   - The graph shows a steep decline in distance to 0, then a rapid increase.
   - This could represent the dog quickly running to the stick (decreasing the distance) and returning to Aly (bringing the distance to zero). However, the final rise in the graph does not match the scenario described.

2. **Graph B**:
   - The graph shows a steady increase in distance, then a steady decrease back to zero.
   - This represents the dog running away from Aly (increasing the distance) and then returning to Aly (decreasing the distance back to zero). Since Aly is moving slowly toward the dog, the dog returns faster than Aly is moving. This matches the scenario well.

3. **Graph C**:
   - This graph shows a gradual increase, followed by a sudden steep rise.
   - This pattern does not correspond to the situation because it suggests a sudden increase in distance at the end, which isn't in line with the described actions.

The best fit for the situation would be **Graph B**, as it shows the distance increasing while the dog runs toward the stick, and then decreasing as the dog returns to Aly.

Do you want more details, or do you have any other questions?

Here are some related questions:
1. How would the graph change if Aly didn't move towards the dog?
2. What if the dog moved slower while returning with the stick?
3. How could this scenario be modeled using a mathematical equation?
4. What is the significance of the slope in distance-time graphs?
5. How would the graph change if Aly was moving faster than the dog?

**Tip**: The steeper the slope in a distance-time graph, the faster the motion represented.

Aly takes his dog to the park. He throws a stick for the dog to catch. The dog runs to collect the stick and bring it back to Aly. While the dog is collecting the stick, Aly walks slowly towards it. Which of the following graphs could show the distance between Aly and the dog?

Explore how distance-time graphs can represent the movement of Aly and his dog. Learn to interpret these graphs and understand concepts such as distance, time, and speed. This example is suitable for students in Grades 6-8.

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