1. I have chosen the Ostrich and the Lion as my two animals with different speeds. The Ostrich has a speed of 40 mph, while the Lion has a speed of 50 mph.
2. To design a fair race, I will give the slower animal, which is the Ostrich, a shorter distance to race. This ensures that both animals have an equal chance of winning if they race at their top speed.
3. Let's define some variables:
- Let dO be the distance the Ostrich travels.
- Let dL be the distance the Lion travels.
- Let vO be the speed of the Ostrich, which is 40 mph.
- Let vL be the speed of the Lion, which is 50 mph.
The time it takes for both animals to complete the race is the same, as it's a fair race. The time can be calculated using the formula: time = distance / speed.
For the Ostrich: time = dO / vO
For the Lion: time = dL / vL
Since the time for both animals is the same, we can set up the following equation:
dO / vO = dL / vL
4. To graph the system, let's create a coordinate plane. The x-axis will represent the distance the Ostrich travels (dO), and the y-axis will represent the distance the Lion travels (dL).
Now, we can solve the equation for dL:
dL = (vL / vO) * dO
Let's substitute the values of the speeds: vL = 50 mph and vO = 40 mph. The equation becomes:
dL = (50 / 40) * dO
dL = (5/4) * dO
Now, we can plot some points on the graph to see how the two animals' distances relate to each other. For example, if the Ostrich travels 80 miles (dO = 80), the Lion would travel:
dL = (5/4) * 80
dL = 100
Plotting the point (80, 100) on the graph, we can see that it lies on a straight line. By plotting more points, we can see that all the points lie on a straight line.
The graph demonstrates that regardless of the distance traveled by the Ostrich, the distance traveled by the Lion is always 1.25 times that of the Ostrich. This ensures that both animals have an equal chance of winning the race.
By designing the race in this way, we have created a fair competition where the slower animal has a shorter distance to cover, giving both animals an equal opportunity to win if they race at their top speeds.