1. Pick two animals to be in a race and answer the following questions. a. Suppose two animals are in a race. Choose two animals from Table 1 and calculate the speed of each animal in yards per second. (6 points)
Example: Kangaroo – 30 miles/hour multiply by 1760 (conversion to yards) divided by 3600 (conversion to seconds). So the speed of a Kangaroo is 14.67 yd/sec.

b. You decide how much of a head start (in yards) the faster animal will offer the slower animal. For each animal, write an equation relating speed (v), distance from the starting line (d), and time (t). (6 points)
Formula:

c. Graph the two equations on the same coordinate plane. (4 points)

d. How long will it take the faster animal to overtake the slower animal? How many yards from the starting line are the animals when the faster animal overtakes the slower animal? (3 points)

e. Reduce the head start by half and repeat parts (c) and (d) from above. (9 points)
(c)

(d) How long will it take the faster animal to overtake the slower animal? How many yards from the starting line are the animals when the faster animal overtakes the slower animal?

2. Pick a third animal and answer the following questions.
a. Choose a third animal. Calculate its speed in yards per second. Compare its speed with the speed of the two animals you chose in Activity 1. (6 points)

b. Decide which two animals should get head starts and how much of a head start each should get. Write three equations relating distance from the starting line to time. (10 points)

c. Graph all three equations on the same coordinate plane. (6 points)

Part B: Which Community Garden Plan? (50 possible points)
The Community Garden Club would like to plant a garden on a small lot in a local neighborhood. One community member, Nancy, suggests a square garden while another member, Juan, suggests a rectangular garden. You will be in charge of determining which of the two gardens would cover the most area while using the least amount of fencing to surround it. You should show all calculations, and give complete explanations.

1. Nancy’s plans for a square garden include an area of (x2 + 12x + 36) m2. Write expressions for the length and width of this square garden. (8 points)

2. The plans for the square garden shows a length of 12 m. What is the width of the square garden? Using the area from problem 1, what is the value of x? What is the total area of this square garden? (9 points)

3. Juan’s plans include a rectangular garden with an area of (x2 + 14x + 24) m2. Write expressions for the length and width of the rectangular garden. (8 points)

4. The plans for the rectangular garden shows a length that is 6 m. longer than the length of the square garden. What is the width of the rectangular garden? How much shorter is the width of the rectangular garden than the square garden? (9 points)

5. Write expressions for the perimeter of each garden in terms of x. Then find each perimeter for the x-values calculated in the previous questions. (8 points)

6. The Community Garden Club would like the garden that covers the most area possible while requiring the least amount of fencing needed to completely surround it. Which garden plan should they choose? Explain your reasoning using the information you calculated for each garden plan. (8 points)
This project can be submitted electronically. Check the Project page in the online course for more detailed instructions.