To compare the rates at which Pilar and Tom are moving, we need to analyze the slopes of their lines on the graph. Since the graph shows the distance from home over time, the slopes of these lines represent their rates of travel, with steeper slopes indicating faster rates.

Step-by-Step Analysis:

1. Determine Slopes:

   • The graph shows both Pilar and Tom starting at the same distance from home but at different rates as indicated by their respective lines' slopes.
   • Pilar’s line is steeper than Tom’s, indicating that her rate of decrease in distance (i.e., her speed) is greater than Tom's.

2. Comparison of Slopes:

   • Pilar’s slope is steeper, which means she is traveling at a faster rate compared to Tom.
   • Therefore, Pilar’s rate is greater than Tom’s rate.

3. Choose the Symbol:

   • Since Pilar’s rate is greater than Tom’s rate, the correct symbol to place in the box is ">".

So, the answer is:

Pilar's rate > Tom's rate.

Would you like to see a detailed explanation of how to calculate and compare slopes directly? Here are some additional questions that could further enhance your understanding:

1. How can the slope of a line be calculated on a distance-time graph?
2. Why does a steeper slope represent a higher rate on a distance-time graph?
3. If Tom had a steeper slope than Pilar, how would we know who is faster?
4. What does it mean if both Pilar and Tom had the same slope on this graph?
5. How can this concept of slope and rate be applied to real-world problems?

Tip: On a distance-time graph, the slope represents the speed. The steeper the slope, the faster the rate of travel.