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.
Your equations, graph, and explanation for your race design will be submitted.
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
I'm choosing pig=11 and squirrel=12
did u get the answer
I would choose something with easy numbers to calculate. you may want to choose ostrich and kangaroo or maybe a lion. Just something with an even number.
To design a fair race for the new video game Animal Tracks, we will use the animals "pig" and "squirrel," which have speeds of 11 mph and 12 mph, respectively.
To create 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 do this by setting up a system of linear equations that represent the distance each animal can travel at their respective speeds.
Let's define the following variables:
x = distance the pig can travel (in miles)
y = distance the squirrel can travel (in miles)
Since the pig is slightly slower, we can give it a shorter distance to race. Let's say the pig travels a distance of x miles, and the squirrel races the longer distance, y miles.
Since speed = distance/time, we can set up the following equations:
For the pig: 11 = x/t (where t is the time it takes for the pig to complete the race)
For the squirrel: 12 = y/t (where t is the time it takes for the squirrel to complete the race)
To eliminate the variable t, we can rearrange the above equations as follows:
x = 11t
y = 12t
Now, let's graph these equations to demonstrate that the race is fair. Since this is a video game, we can choose any convenient values for t.
Let's assume t = 1 hour. Plugging this value into the equations, we get:
x = 11 * 1 = 11
y = 12 * 1 = 12
Plotting these points on a graph, we get:
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x | (11, 12)
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(0, 0) |
Based on the graph, we can see that the point representing the pig (11, 12) and the origin point (0, 0) are on the same line. This indicates that both animals have an equal chance of winning the race if they travel at their maximum speeds.
Therefore, the graph proves that the race is fair since the two animals would finish the race in the same amount of time if they raced at their top speed.
To design a fair race for the video game Animal Tracks, we are given a chart with animals and their speeds. We need to choose two animals with different speeds. In this case, let's choose the pig with a speed of 11 mph and the squirrel with a speed of 12 mph.
Now, we need to design a fair race where both animals have an equal chance of winning if they race at their top speed. The race does not need to be realistic, so we can choose any lengths for the race and assume the animals will run at a constant speed.
To create a fair race, we can give the slower pig a shorter distance to cover compared to the squirrel. Let's say the pig needs to cover a distance of "d" miles, and the squirrel needs to cover a distance of "2d" miles.
Now, we can write a system of two linear equations to represent the distances each animal can travel:
For the squirrel: Distance = Speed x Time
2d = 12t
For the pig:
d = 11t
Here, "t" represents the time taken by both animals to complete the race.
To graph the system, we can plot the two equations on a coordinate plane. The x-axis represents time (t), and the y-axis represents the distance covered.
For the squirrel's equation, when t=0, the distance is also 0. When t=1, the distance would be 2d = 24. This gives us the point (1, 24) on the graph.
For the pig's equation, when t=0, the distance is also 0. When t=1, the distance would be d = 11. This gives us the point (1, 11) on the graph.
Plotting these two points and connecting them with a line gives us a graph.
The graph shows that at any given time t, the distance traveled by the squirrel (2d) is always double the distance traveled by the pig (d).
This means that if both animals race at their top speed, the squirrel will always be twice as far along as the pig, which makes the race fair.
By designing the race with different distances for the animals, we have ensured that they have an equal chance of winning if they race at their top speeds.