Question

b. using a different color for each person, draw a graph of all four peoples journeys (including tylers from the other day).

c. which person is moving the most quickly? how is that reflected in the graph?

are you ready for more?
write equations to represent each persons relationship between time and distance.

Explanation:

Step1: Recall speed - distance - time concept

Speed is given by $v=\frac{d}{t}$, where $d$ is distance and $t$ is time. On a distance - time graph, speed is the slope of the line.

Step2: Analyze slope for part c

The steeper the line on a distance - time graph, the greater the slope, and the faster the person is moving. To find the person moving most quickly, we look for the line with the greatest slope.

Step3: For writing equations

The general form of a linear equation for a distance - time relationship is $d = vt$, where $v$ is the speed (constant for a person moving at a steady rate). We would need data points (co - ordinates on the graph) for each person to calculate their speeds and write the equations.

However, since no data about the actual journeys of the four people (co - ordinates on the graph) is given, we can only explain the general approach.

Answer:

For part c: The person with the steepest line on the distance - time graph is moving the most quickly. The slope of the line represents the speed of the person. For the equations in the "Are you ready for more?" part, without specific data points for each person's journey (such as points on the graph like $(t_1,d_1)$ for different times $t_1$ and distances $d_1$), we cannot write the actual equations. The general form of the equation for a person moving at a constant speed is $d = vt$, where $v$ is the speed of the person and can be calculated as $v=\frac{\Delta d}{\Delta t}$ using two points on their distance - time graph.