Question

Water enters a container at a rate of 2/3 cup per 1/2 minute, and leaks out at a rate of 1/4 cup per 3/4 minute. At what rate is the container filling up?

Answer 1

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.

$\begin{gathered} \text{Entering}-\text{Leaking} \\ \frac{\frac{2}{3}}{\frac{1}{2}}-\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{4}{3}-\frac{1}{3}=\frac{3}{3}=1 \end{gathered}$

Therefore, the rate of the container filling up will be 1 cup/minute.