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 with number 3, as i think i can figure everything else after. My animals i picked are a coyote (runs at 43 mph) and a rabbit (runs at 35 mph)
if fair, they both have the same times.
A1: S1*time=distance1
A2: S2*time=distance2
so those are the fair distances each has to travel. I guess those two equations are the ones asked for. S1, S2 are the speeds of the animals, and d1,d2 are the "fair" distances for each.
To design a fair race for the video game Animal Tracks, you have chosen a coyote and a rabbit as the two animals. The coyote runs at 43 mph, and the rabbit runs at 35 mph.
Step 3: Write a system of two linear equations showing the distance each animal can travel to model the fair race.
Let's define the variables:
Let "d" represent the distance the coyote can travel.
Let "r" represent the distance the rabbit can travel.
Since the race is fair when the two animals finish the race in the same amount of time, we can use the equation: time = distance / speed.
For the coyote:
Time taken by the coyote = d / 43
For the rabbit:
Time taken by the rabbit = r / 35
Since they finish the race at the same time, the time taken by both animals must be equal. Therefore, we can set up the following equation:
d / 43 = r / 35
Simplifying this equation, we can multiply both sides by the least common multiple (LCM) of 43 and 35, which is 1505:
1505 * (d / 43) = 1505 * (r / 35)
Multiplying, we get:
35d = 43r
This equation represents the fair race between the coyote and rabbit.
Now, let's move on to step 4: Graph the system to prove that the two animals have an equal chance of winning the race and explain how the graph proves the race is fair.
To design a fair race, we need to create a system of linear equations that represents the distance each animal can travel. In this case, we have a coyote that runs at 43 mph and a rabbit that runs at 35 mph. Let's define some variables:
Let x represent the distance (in miles) traveled by the coyote.
Let y represent the distance (in miles) traveled by the rabbit.
Since we want both animals to have an equal chance of winning if they race at their top speed, the race is fair when they both finish the race in the same amount of time.
To determine the time it takes for each animal to travel their respective distances, we can use the formula:
Time = Distance / Speed
For the coyote:
Time = x / 43
For the rabbit:
Time = y / 35
Since the race is fair, we want both animals to finish in the same amount of time. Therefore, we can set up the following equation:
x / 43 = y / 35
This is our first equation in the system.
To create the second equation, we can consider the fact that both animals start at the same time and finish the race at the same time. This means that the total time for both animals to complete the race is the same.
We can calculate the time it takes for the coyote as:
Time = Distance / Speed
Time = x / 43
Similarly, for the rabbit, the time can be calculated as:
Time = Distance / Speed
Time = y / 35
To represent the total time for both animals finishing the race, we add the times together:
x / 43 + y / 35
Since we know the total time should be the same for both animals, we can set up the second equation:
x / 43 + y / 35 = t
Here, t represents the total time for both animals to complete the race. This is our second equation in the system.
Therefore, the system of two linear equations representing the distance each animal can travel to model the fair race is:
Equation 1: x / 43 = y / 35
Equation 2: x / 43 + y / 35 = t
Be sure to substitute the appropriate variables and values into the equations based on the chosen speeds of the coyote and the rabbit.
Once you have the equations, you can solve them using algebraic methods such as substitution, elimination, or graphing to find the values of x and y that satisfy both equations.
Then you can proceed to graph the system to prove that the race is fair.