I have a question about these rates given in a related rates question. For example, when it's given that the car is moving at $60\;\text{km/h}$, a balloon is heading up at $2\;\text{m/s}$, a circle's radius is increasing by $5\;\text{cm/s}$, assuming that every property of what I've mentioned is a function of time $(t)$, (distance driven, height, radius) is a function of time, would the derivative of them be the same value for all $t$?
In other words, are these function linear? so that the slope of the curve for all $t$ is the same? Does this imply that the car would of driven $120\;\text{km/s}$ at $t = 2$, or the radius is $10\;\text{cm/s}$ at $t = 2$?
The speeds are all constant in this problem. You need to define the units of $t$ that you are using. If $t$ is measured in hours, a car moving at $60\;\text{km/h}$ will have moved $120\; \text{km}$. It will not be moving at $120\;\text{km/h}$. The same is true for the other cases. You multiply the rate by time to get the position. You need to make sure the units are consistent, so again if $t$ is in hours at $t=2$ the balloon has climbed $7200\; \text m$