Car A and Car B are traveling at constant speeds. The problem asks to determine which car is traveling at a greater speed and how we know. We are given a graph representing the distance traveled by Car A over time, and a table with the distance traveled by Car B over time.

1. Problem Description

Car A and Car B are traveling at constant speeds. The problem asks to determine which car is traveling at a greater speed and how we know. We are given a graph representing the distance traveled by Car A over time, and a table with the distance traveled by Car B over time.

2. Solution Steps

To determine which car is traveling at a greater speed, we need to calculate the speed of each car. Speed is calculated as distance divided by time:

$Speed = \frac{Distance}{Time}$

For Car A, we can pick a point from the graph. For example, at 12 minutes, the distance is 8 miles. Therefore, the speed of Car A is:

$Speed_A = \frac{8 \text{ miles}}{12 \text{ minutes}} = \frac{2}{3} \text{ miles/minute} \approx 0.667 \text{ miles/minute}$

For Car B, we can use any of the data points from the table. Let's use the first data point (15 minutes, 12.5 miles):

$Speed_B = \frac{12.5 \text{ miles}}{15 \text{ minutes}} = \frac{12.5}{15} \text{ miles/minute} = \frac{25}{30} \text{ miles/minute} = \frac{5}{6} \text{ miles/minute} \approx 0.833 \text{ miles/minute}$

Now, we compare the speeds:

$Speed_A \approx 0.667 \text{ miles/minute}$

$Speed_B \approx 0.833 \text{ miles/minute}$

Since $0.833 > 0.667$, Car B is traveling at a greater speed.

3. Final Answer

Car B is traveling at a greater speed. We know this because the calculated speed for Car B ($5/6$ miles/minute) is greater than the calculated speed for Car A ($2/3$ miles/minute).