Question

It takes three identical water pumps 8 hours to fill a pool, What is the constant of variation?

Answer 1

Constant of variation is 24.

Explanation:

Inverse variation states that a relationship between two variables in which the product is remain constant.

If one variable increases then, the other one decreases in proportion so that the product is unchanged,

if y is inversely proportional to x i.e
`y \propto(1)/(x)` or

`y =(k)/(x)` ;where k is the constant of variation.

It is given that 3 identical water pumps takes 8 hours to fill a pool,

since, it will take less time with more pumps, so it is an inverse variation.

By definition of inverse variation;

`time = (k)/(pump)`

Substitute the values to solve for k;

`8 = (k)/(3)`

Multiply by 3 to both sides we get;

`8 * 3 = (k)/(3) * 3`

Simplify:

k = 24

Therefore, the constant of variation is, 24