Question

I need to find the independent and dependent quantity and a statement that describes the relationship between the independent and dependent quantities

Answer 1

We have two relations between length of the trench and time.

Case: we want to know how many feet we can dig in a certain amount of time.

In this case, and in most of the cases, time is the independent quantity.

Therefore, the dependent quantity is the other variable: length of the trench.

For example, we can write a proportional relationship between time (x) and length (y) as:

`y=k\cdot x`

We know that when x=40 min, y=36 ft, according to the machine advertisement.

Then, we can find k as:

`k=(y)/(x)=(36)/(40)=0.9\text{ ft/min}`

And we can write the relation as:

`y=0.9\cdot x`

Answer: the independent quantity is time (in minutes).

NOTE:

Which variable is which depends on what we want to calculate.

If we want to know how much it will take to make a certain length of trench, the independent quantity is the length of the trench. The dependent variable is, in this case, time, as we calculate it from the information about the length of the trench.

If we want to calculate the length of the trench we can dig in a certain time, the independent quantity is time and the dependent quantity is the length of the trench.