Answer:
We conclude that there is NOT a proportional relationship between the distance the blimp travels and the time it travels.
Explanation:
We know if y varies directly with x, we get the equation
y ∝ x
y = kx
k = y/x
where k is called the constant of variation.
In our case we are given:
A blimp travels 255 feet in 1/2 minute
- A blimp travels 255 feet in 1/2minute.
here:
y = 255, and x = 1/2 = 0.5
so substituting y = 255 and x = 0.5 in the equation
k = y/x
k = 255 / 0.5
k = 510
A blimp travels 510 feet in 1/6 minute
here:
y = 510 , and x = 1/6
so substituting y = 510 and x = 1/6 in the equation
k = y/x
k = [510] / [1/6]
k = 3060
A blimp travels 3,060 feet in 1 minute
here
y = 3,060, and x = 1
so substituting y = 3,060 and x = 1 in the equation
k = y/x
k = 3,060 / 1
k = 3060
HERE IS THE VARIATION OF THE CONSTANT OF VARIATION:
A blimp travels 255 feet in 1/2 minute
k = 510
A blimp travels 255 feet in 1/2 minute
k = 3060
A blimp travels 3,060 feet in 1 minute
k = 3060
It is clear that the constant of variation does not remain constant.
Therefore, we conclude that there is NOT a proportional relationship between the distance the blimp travels and the time it travels.