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 as
your portfolio assessment.
i need help i picked 2 animals a mouse which travels at 8mph and a chicken that travels 9mph
Let x represent the distance the mouse travels and let y represent the distance the chicken travels.
The equation for the mouse is 8x = y, and the equation for the chicken is 9y = x.
The graph of the system of equations is a line with a slope of -1. This graph shows that the two animals have an equal chance of winning the race because the line is symmetrical. This means that the distance the mouse travels is equal to the distance the chicken travels, so they will finish the race in the same amount of time.
To design a fair race between a mouse traveling at 8mph and a chicken traveling at 9mph, we can follow these steps:
1. Define the variables:
Let's define d1 as the distance the mouse will travel and d2 as the distance the chicken will travel in the race.
2. Design a fair race:
To create a fair race, we need to ensure that both animals have an equal chance of winning if they both race at their top speeds. Since the chicken is faster, we can give the mouse a head start by making its race distance shorter.
3. Write the equations:
Since the speed of an object can be defined as distance divided by time, we can use the equation speed = distance / time to create our equations.
For the mouse:
Speed of mouse = 8mph = d1 / t1 (Equation 1)
For the chicken:
Speed of chicken = 9mph = d2 / t2 (Equation 2)
Since we want a fair race, we can assume that both the mouse and chicken will take the same amount of time to finish the race.
Therefore, t1 = t2 = t (Equation 3)
4. Graph the system:
To prove that the race is fair, we can graph the equations and see where they intersect.
Let's rearrange Equation 1 to solve for d1:
d1 = 8 * t
Similarly, rearrange Equation 2 to solve for d2:
d2 = 9 * t
Now we can plot these equations on a graph, with d1 on the x-axis and d2 on the y-axis.
The graph will show a line representing the possible combinations of distance traveled by both the mouse and the chicken in a specific time (t).
The intersection point of the two lines will represent the distance (d1 and d2) and time (t) at which both animals will finish the race.
If there is an intersection point on the graph, it means that both animals have an equal chance of winning the race.
The graph proves the race is fair because it shows that there is a point where both animals will reach the finish line simultaneously (or have an equal chance of winning, depending on the game's mechanics).
Submit the equations, graph, and explanation as your portfolio assessment.
To design a fair race between a mouse that travels at 8mph and a chicken that travels at 9mph, you need to create a race where the animals have an equal chance of winning if they race at their top speed. Here's how you can do it:
1. Determine the distance for the race: Since it's a video game, the race can be any length. Let's say you want to keep it simple and choose a distance of 72 miles.
2. Determine the time it takes for each animal to complete the race: To calculate the time taken, you can use the formula: time = distance / speed.
For the mouse: time_mouse = 72 miles / 8 mph = 9 hours.
For the chicken: time_chicken = 72 miles / 9 mph = 8 hours.
3. Write a system of two linear equations representing the race:
Let's define:
x as the distance covered by the mouse.
y as the distance covered by the chicken.
The system of equations can be written as:
x/8 = y/9 (since the time taken by both animals should be equal)
x + y = 72 miles (since the total race distance is 72 miles)
These equations represent a fair race where the ratio of distance to speed is equal for each animal.
4. Graph the system of equations to prove the race is fair:
Plot the graph by assigning values to x and solving for y using the second equation. Then plot the points on a graph and connect them to form a line. If the line intersects at a point, it means both animals have an equal chance of winning.
When you plot the graph, you will see that the line intersects at (32, 40). This means that if the mouse covers a distance of 32 miles, the chicken will cover a distance of 40 miles, and both animals will take the same amount of time to finish the race.
The graph proves that the chosen race design is fair because the line represents all possible solutions where the two animals have an equal chance of winning. In this case, the point of intersection shows that if the mouse and chicken cover the designated distances, they will finish the race at the same time, thus making it fair.