Rate of water entering = 2/3 cup per 1/2 minute
Rate of water leaking = 1/4 cup per 3/4 minute
To get the rate of the container filling up, let's subtract the two rates.
[tex]\begin{gathered} \text{Entering}-\text{Leaking} \\ \frac{\frac{2}{3}}{\frac{1}{2}}-\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{4}{3}-\frac{1}{3}=\frac{3}{3}=1 \end{gathered}[/tex]Therefore, the rate of the container filling up will be 1 cup/minute.
