There is a hiking trail near the town where Han and Jada live that starts at a parking lot and ends at a lake. Han and Jada both decide to hike from the parking lot to the lake and back, but they start their hikes at different times.

At the time that Han reaches the lake and starts to turn back, Jada is 0.6 miles away from the parking lot and hiking at a constant speed of 3.2 miles per hour toward the lake. Han’s distance, , from the parking lot can be expressed as , where represents the time in hours since he left the lake.

1. What is an equation for Jada’s distance from the parking lot as she heads toward the lake?
2. Draw both lines: one representing Han's equation and one representing Jada’s equation. It is important to be very precise! Be careful, work in pencil, and use a straightedge.

   

   <p>Coordinate plane, origin O, with grid. Horizontal axis, time in hours, scale 0 to 1 point 75, by point 25’s. Vertical axis, distance from parking lot in miles, scale 0 to 5, by 1’s.</p>  

3. Find the point where the 2 lines intersect each other. What are the coordinates of this point?
4. How can you check your coordinates using the equations?
5. What do the coordinates mean in this situation?
6. What has to be true about the relationship between these coordinates and Jada’s equation?
7. What has to be true about the relationship between these coordinates and Han’s equation?

A stack of small cups has a height, , in centimeters, of .

A stack of large cups has a height, , in centimeters, of .

1. Graph the equation for each type of cup on the same set of axes. Make sure to label the axes and decide on an appropriate scale.

   

2. For what number of cups will the two stacks have the same height?