Tank Filling: Instantaneous Rate of Flow?

📌 CONCEPT: The problem involves finding the time it takes to fill a tank by considering the rate of filling as a function of time, which is decreasing at a constant rate.

📐 RULE / FORMULA: We can use the concept of integrals to solve this problem by setting up an integral that represents the total amount of water in the tank as a function of time.

💡 WORKED EXAMPLE: Suppose the tank is being filled at an initial rate of 2 litres per minute, decreasing by 0.1 litres per minute every minute. We can set up the integral as ∫[2 - 0.1t]dt from t = 0 to the time it takes to fill the tank. To solve this, we can use the formula for the integral of a linear function: ∫[ax + b]dx = (1/2)ax^2 + bx + C. We can then apply the initial condition that the tank had 150 litres of water in it initially.

⚠️ COMMON MISTAKE: Students often forget to consider the initial condition and the decreasing rate of filling, which can lead to incorrect calculations and answers.