# Thread: How to mathematically derive the rate of change?

1. ## How to mathematically derive the rate of change?

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?

2. ## Re: How to mathematically derive the rate of change?

Water is coming in at the rate $\displaystyle kt$ and going out at rate $\displaystyle kt^{1/2}$. The net rate is $\displaystyle kt- kt^{1/2}$.