UNIT NAME FUNCTIONS Unit 5 Lesson 10 Portfolio

UNIT NAME: FUNCTIONS Unit 5 Lesson 10 Portfolio You cannot submit the example I do in this portfolio for any credit.

Directions: Follow the instructions below to design a fair race for the new video game Animal Tracks. 1. Choose two animals with different speeds. You can choose from the chart that starts at the bottom of this page or do research to choose your own. 2. Design a fair race in which the two animals have an equal chance of winning if they race at their top speed. Here a few tips for your design: a. The race is fair if the two animals could finish the race in the same amount of time. b. You can give the slower animal a shorter distance to race. c. Since this is a video game, the race does not need to be realistic—it can be any length, and the animals can run at a constant speed. 3. Write a system of two linear equations showing the distance each animal can travel to model the fair race. Be sure to define all variables. 4. Graph the system to prove that the two animals have an equal chance of winning the race. Explain how the graph proves the race is fair. Your equations, graph, and explanation for your race design will be submitted as your portfolio assessment.

Animal Speed (mph) • • • • cheetah 70 lion 50 coyote 43 rabbit 35 kangaroo 30 squirrel 12 chicken 9 antelope 61 elk 45 ostrich 40 giraffe 32 elephant 25 pig 11 mouse 8

Chart of the 2 animals in a race Start Equation 1 hour 2 hours 3 hours 4 hours K = 30 h 30 60 90 120 L = 50 h 50 100 150 200 So you can see by the chart that the difference between them in 4 hours would be 80 miles (200 -120). If they started the course at the same time for 4 hours. You would need to give the Kangaroo an 80 mile start. So the equations would be as follows K = 30 h +80 and the L = 50 h (+ 0) no head start.

Kangaroo VS Lion with an 80 m start Equation Start 1 hour 2 hours 3 hours 4 hours 5 hours K=30 h+80 80 110 140 170 200 230 L=50 h+0 50 100 150 200 250 0 300 250 200 Kangaroo 150 Lion 100 50 0 Start 1 hour 2 hours 3 hours 4 hours 5 hours

To check it with the system of equations- substitution K/L= 30 h + 80 L/K = 50 h (+ 0) They should be the same in 4 hours or equal to each other. Set them equal to each other (substitution). 50 h = 30 h + 80 -30 h. 20 h = 80. h = 4 hours

To check it with the system of equations- elimination They should be the same in 4 hours. Put them in Ay + B x = C- to do elimination Y= 30 x + 80 and Y= 50 x (+ 0) Y - 30 x = 80 and Y - 50 x = 0 -(Y - 30 x = 80) Y - 50 x = 0 -Y + 30 x = -80 Y - 30 x = 80 -(Y - 50 x = 0) Y - 30 x = 80 -Y + 50 x = 0