This lesson is optional because it goes beyond the expectations of the standards. Students apply their understanding about constant speed and time-distance ratios to reason about the movement of two objects relative to each other. Students also learn that the two unit rates associated with time-distance ratios can be distinguished as speed and pace.

Although students have solved problems in the context of constant speed (such as finding elapsed time, distance traveled, or rate of travel), the work here is more involved than previous work in that:

• The objects may be moving in opposite directions.
• The distance of interest is between two moving objects, rather than between two fixed points or between a moving object and a fixed point.
• Besides the individual speeds of the two objects, there is another speed—relating how fast one moves toward or away from the other—that can help us make sense of a situation.

In the main activity, students reason about two camels traveling toward one another. In the optional activity, they reason about two people moving away from each other.