Question 9

Explanation

Equating Inflow and Outflow Volumes

The required condition is when the volume of water entering equals the volume of water flowing out.

Substitute the known functions:

Solving the Quadratic Equation

Move all terms to the left side to get the standard quadratic form:

Simplify the equation by dividing both sides by $2$:

Factor the equation. We look for two numbers that multiply to $2100$ and add up to $-100$. These numbers are $-70$ and $-30$.

This gives the solutions:

Thus, the volume of entering water equals the outflowing water at $70$ minutes or $30$ minutes.