1. Adventures of Cluck and Shelley
(Solving a System of Equations)

2. The Situation
Cluck, the chicken, was at the top of Poultry Promontory nesting Shelley, her egg. Shelley, deciding to take off on an adventure, began to roll down the 45-foot slope of Poultry Promontory at a rate of 4 feet per second. Two seconds later Cluck discovered Shelley missing, and began running down the slope to catch Shelley at a rate of 5 feet per second. When will Cluck catch Shelley? Will she be able to catch Shelley before she cracks her noggin’ at the bottom of the hill?
In this situation, x would represent the ________ and y would represent the ___________.
time
distance
The relation is continuous because the x-values can take on every value within an interval.
As opposed to discrete, which would be only specific individual values.

3. The Visualization Shelley Time (sec) Distance (ft) 1 4 2 3 5 6 Cluck
Build tables to represent the distance traveled as a function of time for both Shelley and Cluck.
Shelley
Time (sec)
Distance (ft) 1 4 2 3 5 6
Cluck
Time (sec)
Distance (ft) ? 1 2 3 5 4 6 8 12 16 10 20 15 24 20

4. The Visualization
Graph both of the functions on the same coordinate plane.
Although realistically, Cluck’s distance at times of 0 and 1 seconds is zero feet (since she just sat there!), if we extended the pattern, what would her distances be at 0 and 1 seconds according to this mathematical model? What is the particular linear function for Shelley, assuming a constant rate? (y = mx + b) What is the particular linear function for Cluck, assuming a constant rate? (y = mx + b)
(1, -5) and (0, -10)
y = 4x
Find slope, use point-slope form or known y-intercept.
y = 5x - 10

5. The Mathematics
How far will Shelley and Cluck be after 4 seconds? 6 seconds? 8 seconds? If Shelley is 20 feet down the hill, how long has she been rolling? If Cluck is 35 feet down the hill, how long has she been chasing Shelley?
When and where will Cluck catch Shelley? Will Cluck be in time to save Shelley from cracking her noggin’ at the bottom of the hill? Explain your conclusion.
4 seconds: 16 ft & 10 ft
6 seconds: 24 ft & 20 ft
8 seconds: 32 ft & 30 ft
Extend pattern in table, extend graph, or use the equations.
10 seconds; 40 ft
In the table, where both are at the same distance at the same time.
In the graph, where the lines intersect!
5 seconds
Yes!
The hill is 45 ft high.
7 seconds
(Shelley has been rolling for 9 seconds!) or