1. **Stating the problem:** We have a water tank with total capacity $y$ gallons. Initially, it contains $c$ gallons of water. Water flows into the tank at a rate of $m$ gallons per minute, and $x$ represents the time in minutes. 2. **Formulating the equation:** The amount of water in the tank at time $x$ is the initial amount plus the amount added over time. The amount added is the rate times time. The equation is: $$W(x) = c + mx$$ where $W(x)$ is the water volume at time $x$. 3. **Finding the rate of change (differential equation):** Since $c$ is a constant and $m$ is the rate of inflow, the rate of change of water volume with respect to time is the derivative of $W(x)$: $$\frac{dW}{dx} = \frac{d}{dx}(c + mx) = 0 + m = m$$ This means the water level changes at a constant rate $m$ gallons per minute. 4. **Summary:** - Equation: $$W(x) = c + mx$$ - Rate of change: $$\frac{dW}{dx} = m$$ This differential equation shows the water level increases linearly over time at rate $m$ gallons per minute.