Question

Working together, two identical water pumps can fill a pull in 10 hours. Determine whether quantities (number of pumps and hours) vary directly or inversely and find the constant of variation.

Answer 1

The number of pumps and hours) vary inversely.

The constant of variation is 20.

Step-by-step explanation:

Let x be number of pumps and y be number of hours.

We have been given that working together, two identical water pumps can fill a pull in 10 hours. This means while working alone the pumps will take 2 times as much time to fill the tank.

As we increase number of pumps (x), number of hours (y) is decreasing and as we decrease x our y is increasing, therefore, number of pumps (x) and hours (y) vary inversely.

Since we know that an inversely proportion equation is in form:
`y=(k)/(x)`, where, k is constant of variation.

Upon substituting our given values in above equation we will get,

`10=(k)/(2)`

Upon multiplying both sides of our equation by 2 we will get,

`2*10=2*(k)/(2)`

`20=k`

Therefore, the constant of variation is 20.