Here's the instructions for my portfolio:
1.
Choose
two animals with different speeds. You can choose fro
m 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 spee
d. 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.
It is in Unit 5, & I'd love some help. I wrote this: 25 and 50. Therefore if you do an even number for the race, such as a 4 mile race, you can set the 25MPH elephant half way through the race to start so they will finish at the same time
but I don't know how I'd do the linear equation for it. I've tried going back to review but i don't know what to do. Help?
Sorry, I forgot to mention that the 25 & 50 is the speed to the two animals I chose.
To design a fair race between two animals with different speeds, you need to set up a system of linear equations. Let's go step by step:
Step 1: Choose two animals with different speeds. In this case, you have chosen an animal that moves at 25 mph and another at 50 mph.
Step 2: Design a fair race where both animals have an equal chance of winning if they race at their top speed. To achieve this, you can give the slower animal (25 mph) a shorter distance to race.
Let's assume the distance of the race is d miles. Since we want both animals to finish the race in the same amount of time, we need to figure out the distances they can travel in that time.
Let's say the slower animal, the elephant, starts halfway through the race. This means it will cover half the distance of the race at a constant speed of 25 mph.
Therefore, the distance covered by the elephant is (d/2) miles.
The faster animal, let's say a cheetah, will start at the beginning of the race and will cover the entire distance of the race at a speed of 50 mph.
Therefore, the distance covered by the cheetah is d miles.
Step 3: Write a system of two linear equations to model the fair race. In this case, the equations will represent the distances covered by each animal.
Let's define these variables:
d = total distance of the race
d_e = distance covered by the elephant
d_c = distance covered by the cheetah
The system of equations would look like this:
d_c = d
d_e = d/2
Step 4: Graph the system of equations to prove that the two animals have an equal chance of winning the race.
To graph this system, we can set up a coordinate plane with d_c (distance covered by cheetah) on the x-axis and d_e (distance covered by elephant) on the y-axis.
Plot the points (d, d/2) and (d, d) on the graph. Draw a line connecting these two points.
The line represents all possible combinations of distances covered by the cheetah and the elephant for a fair race. Any point on this line indicates a scenario where both animals have an equal chance of winning.
The graph proves the race is fair because any point on the line represents a combination of distances where the two animals would finish the race at the same time.
I hope this step-by-step explanation helps you with your portfolio!
To design a fair race between an elephant with a speed of 25 mph and another animal with a speed of 50 mph, you need to establish a situation where both animals have an equal chance of winning. The goal is to ensure that both animals take the same amount of time to complete the race. Here's how you can achieve that:
Step 1: Define the variables
Let's use the variable 't' to represent the time taken by both animals to complete the race.
Step 2: Determine the distance traveled by each animal
Since the animals are running at a constant speed, you can calculate the distance traveled by multiplying their respective speeds (miles per hour) by the time taken (hours). Let's use the variable 'd' to represent the distance traveled by each animal.
For the elephant: d = 25t (distance traveled equals speed multiplied by time)
For the other animal: d = 50t
Step 3: Set the distance for each animal
To make the race fair, you can give the slower animal (elephant) a shorter distance to race. Let's say the total race distance is 'x' miles. The other animal will cover the entire distance, but the elephant will only cover a fraction of it. Let's use the variable 'f' (0 < f < 1) to represent the fraction of the race distance covered by the elephant.
The distance covered by the elephant: d = f * x
The distance covered by the other animal: d = x
Step 4: Set up the system of linear equations
Now, we can create a system of equations based on the distances traveled by each animal:
Equation 1: 25t = f * x
Equation 2: 50t = x
These equations express the relationship between the time taken, the distance covered, and the race distance.
Step 5: Solve and graph the system of equations
To prove that the race is fair, we need to solve the system of equations and graph the results.
By rearranging Equation 1, we find that f = (25t) / x. Substituting this value into Equation 2:
50t = x
Now, we can solve for t:
t = x / 50
Substituting this value of t into Equation 1:
f = (25(x / 50)) / x
f = 0.5
This indicates that the fraction of the race distance covered by the elephant should be half, regardless of the race distance chosen.
Graphically, you can plot the distance traveled on the y-axis and the time on the x-axis. Plot both equations on the same graph, and you should see that they intersect at a point where both animals complete the race in the same amount of time. This intersection point confirms that the race is fair and that both animals have an equal chance of winning.
Note: The above explanation assumes a simplified situation for the purpose of a fair race design in a video game. In reality, variables such as acceleration, fatigue, etc., can significantly affect the outcome of a race.