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

Answer:

$9\frac{1}{3}$ months.

Step-by-step 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:

$1\frac{1}{3}=k\cdot 1$

$\frac{4}{3}=k$

The equation $m=\frac{4}{3}g$ 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.

$m=\frac{4}{3}*7$

$m=\frac{4*7}{3}$

$m=\frac{28}{3}$

$m=9\frac{1}{3}$

Therefore, it will take $9\frac{1}{3}$ months for the faucet to leak 7 gallons of water.