Here is a diagram that shows Doug's distance in miles from his nearest bus stop, relative to the time of day (in hours) that the bus arrives (click to stop; double-click to start). The top line's length represents his distance, where one unit on the grid is one mile on the blue segment; the bottom line's length represents hours from the bus' arrival, where one unit on the grid is one hour on the green segment.
Interpret the diagram. Clarify any issues that must be settled before the diagram makes complete sense (e.g., What does the length of the green segment represent? What does it mean that the blue segment moves from the left of the vertical line to the right of the vertical line? Is an hour for the bus the same as an hour for Doug? Etc.). Keep a list of the issues and how you settled them.
What is the relationship between Doug's distance and the number of hours before or after the bus arrives at the bus stop? Is this different from the relationship between his distance and the number of hours before he arrives at the bus stop?
Does Doug move at a constant speed? How do you know? If so, at what speed does Doug move?
How many hours away from the bus stop is Doug when the bus arrives at the stop?
How might you change the diagram to reflect that Doug actually gets on a bus?
Make up an entirely different scenario that fits this diagram. Change questions 1-4 to reflect the new scenario.