Question

A vehicle travels 250 feet every three seconds find the value of the ratio, the unit rate, and the constant proportionality. How are they related?

Answer 1

Answer:

The ratio, the unit rate and the constant of proportionality are same but with different name.

Step-by-step explanation:

A vehicle travels 250 feet every three seconds.

(i) So, the ratio is $\frac{250}{3}$  feet/seconds.

(ii) The unit rate means the rate of change of distance with respect to unit time,

The vehicle in three seconds moves by 250 feet.

Hence, the vehicle in one second will move by $\frac{250}{3}$ feet.

Therefore, the unit rate is $\frac{250}{3}$ feet/seconds.

(iii) The relation between the distance traveled (d) and the time of travel (T) is proportional.

So, D ∝ T, ⇒ D = kT ......... (1) {Where, k is the constant of proportionality}

Since D = 250 feet at T = 3 seconds

So, from equation (1), $k = \frac{D}{T} = \frac{250}{3}$  feet/seconds.

Therefore, from the above explanation it is clear that the ratio, the unit rate and the constant of proportionality are same but with different name. (Answer)