I am just stating, I do not want people to give me the answers to this, I would just like to have someone walk through it with me. Just making that clear, thank you.
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
The 2 animals I am picking is an ostrich and lion.
Unfortunately, No one knows..
Great! Let's work through the steps together to design a fair race between the ostrich and lion.
Step 1: Choose two animals with different speeds. You have already chosen the ostrich and lion.
Step 2: Design a fair race. In order for the race to be fair, we need to ensure that both animals have an equal chance of winning if they race at their top speed. Since this is a video game, the race does not need to be realistic in terms of distance or how fast the animals run. We can adjust the race distance to make it fair.
To do this, we can assign a variable for the distance the ostrich needs to run and another variable for the distance the lion needs to run. Let's call these variables "d_ostrich" and "d_lion," respectively.
Since the lion is slower than the ostrich, we can give the lion a head start by reducing the distance it needs to run compared to the ostrich. This way, both animals will have an equal chance of winning if they race at their top speeds.
Step 3: Write a system of two linear equations. We can write the equations based on the distances the ostrich and lion need to run. Let's say the ostrich's top speed is represented by "s_ostrich" mph, and the lion's top speed is represented by "s_lion" mph.
The equations can be written as:
Distance the ostrich can run: d_ostrich = s_ostrich * t
Distance the lion can run: d_lion = s_lion * t
Note: "t" represents the time it takes for both animals to finish the race.
Step 4: Graph the system to prove the race is fair. To graph the system, we need to assign values to the variables and plot the points on a graph. Since the speed values are not given, let's assume the ostrich has a top speed of 40 mph and the lion has a top speed of 30 mph.
Using these values, our equations become:
d_ostrich = 40 * t
d_lion = 30 * t
To graph the equations, we can plot the distance (y-axis) against time (x-axis). We can choose different values of "t" and calculate the corresponding distances for both the ostrich and lion. Then, plot these points on the graph.
For example, if we assume t = 2:
d_ostrich = 40 * 2 = 80
d_lion = 30 * 2 = 60
Using more values for "t", we can plot multiple points to create a line for each animal. If the two lines intersect at any point, it means the animals have equal chances of winning.
Explain how the graph proves the race is fair:
If the lines representing the distances the ostrich and lion can travel intersect, it means that at that specific point, both animals would have traveled the same distance within the same time. This intersection point represents a fair race because both animals have an equal chance of winning at that point.
I hope this helps you design a fair race between the ostrich and lion for the Animal Tracks video game!
To design a fair race between an ostrich and a lion in the Animal Tracks video game, we need to ensure that both animals have an equal chance of winning if they race at their top speed.
Here's how we can approach it:
1. Choose the two animals:
We have already chosen the ostrich and the lion.
2. Design a fair race:
The race should be fair if the two animals could finish the race in the same amount of time. Since the race does not need to be realistic, we can choose any length for the race.
Let's say we choose a race distance of 1000 meters.
3. Write a system of linear equations:
We want to find two linear equations that will represent the distance each animal can travel within the race distance.
Let's denote the distance the ostrich can travel as 'D_o' and the distance the lion can travel as 'D_l'.
Since both animals will be racing at their top speed, we can use the formula:
Distance = Speed * Time
For the ostrich, we have:
D_o = 40 * Time_o
For the lion, we have:
D_l = 50 * Time_l
Here, 'Time_o' represents the time taken by the ostrich and 'Time_l' represents the time taken by the lion to complete the race.
4. Graph the system of equations:
To graph the system of equations, we need to rewrite them in slope-intercept form (y = mx + c), where 'y' represents the distance and 'x' represents time.
Rearranging the equations, we have:
Distance ostrich: y = 40x (equation 1)
Distance lion: y = 50x (equation 2)
From the equations, we see that the slopes of both lines are 40 and 50, respectively.
Graph these two lines on a coordinate plane, with 'x' representing time and 'y' representing distance.
5. Explanation of fairness:
The graph will show the intersection point of the two lines. If the intersection point exists, it means that there is a common solution to the system of equations. This represents a situation where both animals can cover the same distance in the same amount of time.
If the intersection point does not exist, it would mean that one animal would always cover a greater distance in the given race distance, giving an unfair advantage.
To determine if the lines intersect, check if they have the same slope and different y-intercepts. If so, they will intersect and the race is fair.
If the lines are parallel, they will never intersect, indicating an unfair race.
By following these steps, you should be able to design a fair race between the ostrich and the lion in the Animal Tracks video game. Remember to submit your equations, graph, and an explanation of how the graph proves the race is fair.