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 are 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.
Choose two of the animals below:
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
I will choose the cheetah and the elephant for this fair race.
1. The cheetah has a speed of 70mph, while the elephant has a speed of 25mph.
2. To design a fair race, we can give the cheetah a shorter distance to run than the elephant. Let's say the cheetah will run a distance of 2000 meters, while the elephant will run a distance of 5000 meters.
3. Let x be the time it takes for the cheetah to run 2000 meters, and y be the time it takes for the elephant to run 5000 meters. We can model the fair race with the following system of linear equations:
2000 = 70x (distance = speed x time for the cheetah)
5000 = 25y (distance = speed x time for the elephant)
4. To graph this system, we can use the slope-intercept form of the equations:
x = 2000/70 = 28.57 (solve for x)
y = 5000/25 = 200 (solve for y)
The graph of the system will have the cheetah's distance on the x-axis and the elephant's distance on the y-axis. The equations represent two lines that intersect at the point (2000, 5000). This point is the solution to the system and shows that if the cheetah runs 2000 meters and the elephant runs 5000 meters, they will finish the race at the same time. Therefore, the race is fair.
The graph proves the race is fair because the point of intersection shows the distance at which both animals will finish the race at the same time. Additionally, we can see from the slope of the lines that the cheetah is traveling at a much faster speed than the elephant, so it makes sense that the cheetah would need to run a shorter distance to make the race fair.
Math is a valuable skill for many workers at their jobs. List two specific examples where math is used in the workplace.
1. Architects and engineers use math extensively in their work, including calculating loads and stresses, determining measurements for building materials, and designing complex structures that must adhere to strict building codes and safety standards.
2. Financial analysts and accountants use math to perform various calculations, such as determining profitability and return on investment, analyzing market trends, creating budgets and projections, and ensuring that all financial records are accurate and meet legal and regulatory requirements.
I will randomly select two animals for the race: cheetah and squirrel.
To design a fair race, we need to ensure that both animals have an equal chance of winning if they race at their top speed. We can achieve this by giving the slower animal, the squirrel, a shorter distance to race.
Let's assume the cheetah can run at its top speed, 70 mph, for distance c, and the squirrel can run at its top speed, 12 mph, for distance s.
Next, we'll write a system of linear equations to model the fair race:
1) c/70 = s/12
This equation states that the time it takes for the cheetah to run its distance c is equal to the time it takes for the squirrel to run its distance s. The ratios of the distances to the speeds must be equal for a fair race.
2) c + s = total race distance
This equation states that the sum of the distances the cheetah and squirrel run must be equal to the total race distance.
Now, let's graph the system of equations to prove that the two animals have an equal chance of winning the race.
Let's assume the total race distance is 1000 meters.
Using equation 2, we can rewrite it as:
c + s = 1000
s = 1000 - c
Now we substitute the value of s in equation 1:
c/70 = (1000 - c)/12
To solve for c, we need to isolate it by cross multiplying:
12c = 70(1000 - c)
12c = 70,000 - 70c
82c = 70,000
c ≈ 853.66
Now substitute the value of c back into equation 2 to find s:
853.66 + s = 1000
s ≈ 146.34
So the cheetah would run approximately 853.66 meters, and the squirrel would run approximately 146.34 meters.
Now, let's plot this on a graph.
The x-axis represents the distance the cheetah runs (c), and the y-axis represents the distance the squirrel runs (s).
Plotting the two points: (853.66, 146.34) and (0, 1000), we can draw a line connecting these two points.
The graph shows that both animals have an equal chance of winning the race because any point on the line represents a fair race. The line represents all possible combinations of distances that satisfy the condition that both animals finish the race in the same amount of time.
This proves that the race is fair, as the animals have an equal chance of winning if they race at their top speed.