A blimp travels 255 feet in 1/2minute, 510 feet in 1/6 minute, and 3,060 feet in 1 minute. is there or is there not a proportional relationship between the distance the blimp travels and the time it travels.

We conclude that there is NOT a proportional relationship between the distance the blimp travels and the time it travels.

Step-by-step 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

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.