Directions: Follow the instructions below to design a fair race for the new video
game Animal Tracks.
1. Choose two animals at 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.
I HAVE NO IDEA WHAT TO DO!!! HELP PLEASE...
this is "pre"-algebra?
Sure looks like algebra to me.
You can start by considering something like
the fast animal runs twice as fast, so they can finish at the same time if the fast animal has to run twice as far, or has to wait before starting.
he can be made to run farther if the slower animal has a head start, or gets to run on the inside, while the faster animal has to run on the outside.
I'm sure with a little thought you can devise a scheme.
No worries, I can help you with that! Let's break down the steps one by one:
Step 1: Choose two animals at different speeds.
You can either choose from the provided chart or do some independent research to find animals with different speeds. For the sake of example, let's choose a cheetah, known for its speed, and a sloth, known for its slowness.
Step 2: Design a fair race.
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 a shorter distance to race. Let's say the cheetah can travel at a speed of 70 meters per second, and the sloth can travel at a speed of 2 meters per second. We can give the sloth a shorter distance, such as 100 meters, and the cheetah a longer distance, such as 1000 meters. This way, if both animals run at their top speed, they could finish the race in the same amount of time.
Step 3: Write a system of two linear equations.
Let's define the variables:
- Dc as the distance the cheetah needs to run
- Ds as the distance the sloth needs to run
Since distance (D) is equal to speed (S) multiplied by time (T), we can write the following equations:
For the cheetah: Dc = 70T
For the sloth: Ds = 2T
Step 4: Graph the system.
To graph this system, we'll plot the distance (y-axis) against time (x-axis) for both animals.
For the cheetah: Dc = 70T
For the sloth: Ds = 2T
The graph will show the distance covered by each animal over time. The point where the two lines intersect represents the time at which the two animals would finish the race.
If the intersection point occurs at the same time on the x-axis, it means both animals have an equal chance of winning the race. The graph visually represents the fairness of the race.
I hope this helps! Let me know if you have any further questions.
Designing a fair race for the video game Animal Tracks requires choosing two animals at different speeds and designing a race where both animals have an equal chance of winning if they race at their top speed.
Here's how you can approach this task step by step:
1. Choose two animals: You can either choose animals from the provided chart or conduct research to find animals with different speeds. For example, you could choose a cheetah (fast) and a tortoise (slow) as your two animals.
2. Design a fair race: To create a fair race, you can give the slower animal a shorter distance to race. The key is to ensure that both animals can finish the race in the same amount of time. Since this is a video game, you can make the race distance and speed of the animals as per your preference. For instance, you could have the cheetah run 1000 meters and the tortoise run 500 meters.
3. Write a system of linear equations: A system of two linear equations can be used to represent the distances covered by each animal in the race. Let's use the example of the cheetah and tortoise race:
Let:
- dC = Distance covered by the cheetah (in meters)
- dT = Distance covered by the tortoise (in meters)
Assuming that the cheetah's speed is x meters per second and the tortoise's speed is y meters per second, we can write the following equations:
dC = x * t
dT = y * t
In these equations, t represents the time taken by both animals to finish the race. Since the race is fair, both animals should finish at the same time.
4. Graph the system: To graph the system of equations, represent the distances on the x-axis and the time on the y-axis. Each equation will have a linear graph. Plot the points on the graph and check if they intersect, which would indicate that both animals finish the race at the same time. If the graphs intersect, it proves that the race is fair since both animals have an equal chance of winning.
Remember, the specific values chosen for speeds and distances can vary as long as they meet the condition of providing an equal chance for both animals to win.
I hope this explanation helps you design and understand a fair race for the Animal Tracks video game!