21. Water flows into a tank at a rate of 3 litres per minute. (a) If the tank fills completely in 450 seconds, what is the capacity of the tank in ml ? A hole is drilled in the bottom of the tank. Water flows out of the hole at a rate of 60 ml per second. (b) How long will the tank take to drain completely if the flow of water in continues at the same rate?

To solve the problem, we will break it down into two parts: (a) calculating the capacity of the tank in milliliters, and (b) determining how long it will take to drain the tank completely. ### Part (a) 1. **Flow rate into the tank**: 3 liters per minute. 2. **Convert the flow rate to liters per second**: \[ 3 \text{ liters/minute} = \frac{3 \text{ liters}}{60 \text{ seconds}} = 0.05 \text{ liters/second} \] 3. **Time to fill the tank**: 450 seconds. 4. **Calculate the total volume of water that fills the tank**: \[ \text{Volume} = \text{Flow rate} \times \text{Time} = 0.05 \text{ liters/second} \times 450 \text{ seconds} = 22.5 \text{ liters} \] 5. **Convert liters to milliliters** (1 liter = 1000 milliliters): \[ 22.5 \text{ liters} = 22.5 \times 1000 \text{ ml} = 22500 \text{ ml} \] So, the capacity of the tank is **22500 ml**. ### Part (b) 1. **Flow rate out of the hole**: 60 ml per second. 2. **Total volume of the tank**: 22500 ml (from part (a)). 3. **Calculate the time to drain the tank completely**: \[ \text{Time} = \frac{\text{Volume}}{\text{Flow rate out}} = \frac{22500 \text{ ml}}{60 \text{ ml/second}} = 375 \text{ seconds} \] Thus, the tank will take **375 seconds** to drain completely if the flow of water in continues at the same rate.