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The problem asks which graph best represents the distance Tamara travels each day, given that she runs on some days and walks on others. The key points to consider are:

- When Tamara runs, she likely covers more distance in less time compared to when she walks.
- The graph should reflect two different speeds: one for running (steeper slope) and one for walking (less steep slope).

Let's analyze the provided graph options:

1. **Graph 1** (Flat line): This graph shows no change in distance over time, which means no movement at all. This does not apply to Tamara because she either runs or walks, both involving movement.

2. **Graph 2** (Two different slopes): This graph shows two distinct slopes—one steep and one less steep. This could represent Tamara running (steep slope) for part of the time and walking (gentler slope) for the other part. This fits the scenario described.

3. **Graph 3** (Triangle): This graph shows an increase and then a decrease in distance over time. This suggests that Tamara would first travel a certain distance and then return to her starting point, which does not match the problem's description.

4. **Graph 4** (Straight line with constant slope): This graph shows a constant increase in distance over time, which would represent a consistent pace, but it doesn't reflect the change between walking and running.

Given the information, **Graph 2** best represents the situation where Tamara both runs and walks, as it shows different rates of travel (two different slopes) in one trip.

Would you like more details or have any other questions?

Here are five related questions for deeper understanding:
1. How can you identify changes in speed from a distance-time graph?
2. What does the slope of a distance-time graph represent in terms of speed?
3. How would the graph look if Tamara only walked, without running?
4. What would the graph look like if Tamara stopped to rest during her route?
5. How would a velocity-time graph differ from this distance-time graph?

**Tip:** In a distance-time graph, a steeper slope always indicates faster movement.

Tamara either runs or walks the same route each day. Last month she ran half the days and walked the other days. Which graph best represents the distance she travels each day?

Analyze the distance-time graph to determine the correct representation of Tamara’s running and walking patterns. Learn about slopes and rates of change, suitable for students in Grades 6-8.

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