Answer:
Constant of variation is 24.
Step-by-step 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 [tex]y \propto\frac{1}{x}[/tex] or
[tex]y =\frac{k}{x}[/tex] ;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;
[tex]time = \frac{k}{pump}[/tex]
Substitute the values to solve for k;
[tex]8 = \frac{k}{3}[/tex]
Multiply by 3 to both sides we get;
[tex]8 \times 3 = \frac{k}{3} \times 3[/tex]
Simplify:
k = 24
Therefore, the constant of variation is, 24
