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.
