Consider we are filling a tank of water with a rate of $kt$ where $k$ is a constant. The tank has a leakage with the rate of $kt^{1/2}$. How can we mathematically derive the overall rate of filling?
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Water is coming in at the rate $\displaystyle kt$ and going out at rate $\displaystyle kt^{1/2}$. The net rate is $\displaystyle kt- kt^{1/2}$.