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
To design a fair race between a mouse and a chicken, you need to create a race where both animals travel at their top speeds and finish the race in the same amount of time. Since the mouse has a speed of 8 mph and the chicken has a speed of 9 mph, you can give the slower animal (the mouse) a shorter distance to race.
Let's use the formula Time = Distance/Speed for each animal.
1) For the mouse, let's represent the distance it needs to travel as Dm. Since the mouse moves at 8 mph, the time it takes to finish the race is Tm = Dm/8.
2) For the chicken, let's represent the distance it needs to travel as Dc. Since the chicken moves at 9 mph, the time it takes to finish the race is Tc = Dc/9.
In order to make the race fair, we want the time it takes for the mouse and the chicken to be equal (Tm = Tc).
So, we have the following two linear equations:
Tm = Dm / 8
Tc = Dc / 9
Tm = Tc
Replacing Tm and Tc from the first two equations:
Dm / 8 = Dc / 9
Now, we need to find a suitable distance for both animals. Let's assume the chicken will run 9 miles.
9 = Dc / 9
Dc = 81
Now, plugging this value into the equation:
Dm / 8 = 81 / 9
Dm / 8 = 9
Dm = 72
So the mouse will have to run 72 miles while the chicken runs 81 miles.
The linear equations for this fair race are:
Dm = 8Tm
Dc = 9Tc
Graph these equations to show that the animals have an equal chance of winning the race. At the point where the two lines intersect on the graph, both the mouse and chicken finish the race at the same time, proving that the race is fair.
To design a fair race between a mouse and a chicken, you can follow these steps:
1. Determine the race distance: As the race does not need to be realistic, you can choose any distance for the race. Let's say the race distance is 72 miles.
2. Calculate the time it takes for each animal to complete the race: Using the formula: Time = Distance / Speed, we can calculate the time it takes for the mouse and the chicken to complete the race.
Mouse Time = 72 miles / 8 mph = 9 hours
Chicken Time = 72 miles / 9 mph = 8 hours
3. Adjust the race distance to make it fair: Since the mouse is slower, we can decrease the race distance for the mouse to make the race fair. Let's assume the mouse race distance is "x" miles.
4. Write the system of linear equations:
Let x be the distance traveled by the mouse (in miles), and y be the distance traveled by the chicken (in miles).
Equations:
Mouse: x/8 = 9
Chicken: y/9 = 8
5. Solve the system of equations to find the distances traveled by each animal:
Mouse: x = 8 * 9 = 72 miles
Chicken: y = 9 * 8 = 72 miles
The mouse will travel 72 miles and the chicken will also travel 72 miles.
6. Graph the system of equations to prove the race is fair:
On a graph, plot the points (72, 72) for both the mouse and the chicken. Connect the points with a line. Since both animals will reach the finish line at the same time, the lines representing their distances on the graph will be parallel.
The graph shows that at every point along the lines, the distances traveled by the mouse and the chicken are equal, ensuring a fair race.
By designing a race where the mouse covers a distance of 72 miles and the chicken covers the same distance, both animals have an equal chance of winning the race. The graph confirms this fairness by showing parallel lines representing their distances.
To design a fair race between a mouse traveling at 8mph and a chicken traveling at 9mph, you can follow these steps:
Step 1: Define the variables
Let's define the following variables for our equations:
- m = distance the mouse can travel (in any unit, let's say yards)
- c = distance the chicken can travel (in the same unit as m)
Step 2: Design a fair race
In order to make the race fair, we want to ensure that both animals have an equal chance of winning if they race at their top speed. To achieve this, we can manipulate the distance each animal needs to travel.
Since the chicken is faster, we can give the mouse a head start. For example, let's say we want the mouse to have a 1-yard head start. Therefore, the distance for the mouse (m) would be greater than the distance for the chicken (c) by 1 yard.
Step 3: Write the system of equations
Based on our fair race design, we can write the following system of equations:
m = c + 1 (Equation 1 - distance for the mouse)
m/8 = c/9 (Equation 2 - time taken for the mouse and chicken)
The first equation represents the distance each animal can travel, where the mouse distance (m) is equal to the chicken distance (c) plus 1 yard (due to the head start).
The second equation represents the time taken for both animals to travel their respective distances. Since distance equals speed multiplied by time, we can set the ratios of distance to speed to be equal for both animals.
Step 4: Graph the system to prove fairness
To graph this system, we can plot the variables m and c on a coordinate plane. The x-axis can represent m, and the y-axis can represent c. Plotting both equations on this graph will help visualize the fairness of the race.
Equation 1 (m = c + 1) can be graphed as a straight line with a positive slope, passing through the point (1,0).
Equation 2 (m/8 = c/9) can be graphed as a line with a negative slope, passing through the origin (0,0).
The point where the two lines intersect will represent the solution, indicating the distance at which the race is fair.
The fact that these lines intersect proves that there exists a point where both animals have an equal chance of winning the race.
By following these steps, you should be able to design a fair race for the video game Animal Tracks between a mouse traveling at 8mph and a chicken traveling at 9mph.