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
elephant | 25
pig | 11
mouse | 8
I have chose my two animals which are the pig and the squirrel, but I don't how to draw the graph or equation. Please help and explain cause I don't get it
The pig travels 11miles per hour. If you do a distance time graph. Thus the time goes along the x-axis and the distance goes up the y-axis.
So for the pig you would plot the points (1,11) then (2,22) then (3,33) etc.
The equation is in the form y=mx+b where b is the base value (where the graph crosses the y-axis) and m is the slope : )
How is this for a start??
Very good! Thank u so much!!! This really confused me but I think I get it now! Thx again! :)
I need the same thing but with the Coyote and the Ostrich
No
you do the exact same thing just fill in the numbers for your animals
Well, here's a funny idea for your race: a Pig vs a Squirrel! Let's see how we can make it fair.
First, let's define some variables:
Let 'x' represent the distance the pig will race (in miles).
Let 'y' represent the distance the squirrel will race (in miles).
Since the pig is slower, we can give it a shorter distance to race. Let's say the squirrel will run twice the distance the pig runs.
Now, let's set up the equations:
Equation 1: x = d (distance in miles the pig runs)
Equation 2: y = 2d (distance in miles the squirrel runs, twice the distance the pig runs)
Now, it's graphing time!
To graph this system of equations, we can use the x-axis to represent the distance raced by the pig and the y-axis to represent the distance raced by the squirrel. We'll assume the maximum value for both distances is 10 miles.
Let's plug in some random values for d (distance):
- For the pig, let's say it runs 3 miles. So, x = 3.
- For the squirrel, its distance is twice that of the pig, so y = 2 * 3 = 6.
Now plot these coordinates: (3, 6).
Repeat this process for some other values of d and plot the coordinates:
- For the pig: d = 1, x = 1. And for the squirrel: y = 2 * 1 = 2. Plot the coordinate (1, 2).
- For the pig: d = 5, x = 5. And for the squirrel: y = 2 * 5 = 10. Plot the coordinate (5, 10).
Finally, connect the dots to create a line on the graph. You'll see that the line should pass through the origin (0, 0), because if the pig runs 0 miles, the squirrel would run 0 miles as well.
Now, let's see how this graph proves the race is fair. If we compare any point on the line, let's say (x, y), we can see that x = d, and y = 2d. Since the squirrel always runs twice the distance of the pig, they will finish at the same time if they both race at their top speeds.
So, the graph shows that for any point on the line, the pig and squirrel have an equal chance of winning the race. It's a fair race with a comedic twist!
I hope this helps! Good luck with your project!
To design a fair race between the pig and the squirrel, we can give the pig a shorter distance to race since it is slower than the squirrel. Let's denote the distance the pig will run as P, and the distance the squirrel will run as S.
To create a fair race, we need to ensure that the time taken by both animals to complete their respective distances is the same. The formula to calculate time is time = distance / speed.
For the pig:
time taken by the pig = P / speed of the pig
For the squirrel:
time taken by the squirrel = S / speed of the squirrel
Since we want both animals to have an equal chance of winning, the time taken by both animals should be the same.
Equating the two equations, we get:
P / speed of the pig = S / speed of the squirrel
Now let's assign specific values to the speeds to create a race. Let's say the speed of the pig is 11 mph, and the speed of the squirrel is 12 mph.
Our equation becomes:
P / 11 = S / 12
To further simplify the equation, we can multiply both sides by the least common multiple of 11 and 12, which is 132. This will eliminate the fractions:
12P = 11S
Now we have our system of two linear equations:
12P - 11S = 0
Let's graph this system to see if the pig and squirrel have an equal chance of winning the race:
First, choose reasonable values for P and solve for S using the equation 12P - 11S = 0. For example, let's assume P = 8.
12 * 8 - 11S = 0
96 - 11S = 0
11S = 96
S = 96 / 11
Now we have one point on the graph, which is (8, 96/11).
Next, choose another value for P and repeat the process to find another point on the graph. For example, let's assume P = 12.
12 * 12 - 11S = 0
144 - 11S = 0
11S = 144
S = 144 / 11
Now we have the second point on the graph, which is (12, 144/11).
Plot these two points on a graph with P on the x-axis and S on the y-axis. Connect the points with a straight line.
The graph demonstrates that for any combination of P and S on the line, the time taken by the pig and the squirrel will be the same. Therefore, both animals have an equal chance of winning the race, making it fair.