Solution:

1. To find the time it takes for the sheriff to catch the robber, we need to set up an equation based on the distance they travel. Let’s assume that the distance between them at the start is d km. Then, the equation is:

distance traveled by sheriff = distance traveled by robber + d

Let t be the time it takes for the sheriff to catch the robber. Then, the distance traveled by the sheriff is 150t km, and the distance traveled by the robber is also 150t km. Substituting these values in the equation, we get:

150t = 150t + d

Simplifying, we get:

d = 0

This means that the distance between them at the start is zero, i.e., they start from the same point.

1. To find the distance they have traveled when the sheriff catches the robber, we can use either the distance traveled by the sheriff or the robber. Let’s use the distance traveled by the sheriff, which is 150t km. Substituting the value of t from the previous equation, we get:

distance traveled = 150t = 150(0) = 0 km

This means that they have traveled zero distance when the sheriff catches the robber.

1. In terms of algebra, the equation we obtained has only one solution, which is t = 0. This means that the sheriff catches the robber at the same instant they start moving.

2. The graph of the solution is a straight line passing through the origin, with slope 150 (representing the speed of the cars) and intercept 0 (representing the initial distance between them). The graph is shown below: