Question

a broken faucet leaks one gallon of water every 1 1/3 months. the amount of months that pass, m , varies directly with the amount of gallons that are leaked, g. find the equation that models this direct variation. How many months will it take for the faucet to leak 7 gallons of water?

Answer 1

nine months, and a third of a month

Answer 2

`9(1)/(3)` months.

Explanation:

We have been a broken faucet leaks one gallon of water every 1 1/3 months.

Since the amount of months that pass, m , varies directly with the amount of gallons that are leaked, g, so we can represent this information in a equation as:

`m=k\cdot g`

Substitute the given values:

`1(1)/(3)=k\cdot 1`

`(4)/(3)=k`

The equation
`m=(4)/(3)g` represents the given scenario.

To find the number of months it will take for the faucet to leak 7 gallons of water, we will substitute
`g=7` in our equation.

`m=(4)/(3)*7`

`m=(4*7)/(3)`

`m=(28)/(3)`

`m=9(1)/(3)`

Therefore, it will take
`9(1)/(3)` months for the faucet to leak 7 gallons of water.