3.1.2 Example Problem To Be Solved

A bathtub initially contains 40 litres of water. Water runs out at a steady rate of 30 litres per minute. Initially, water flows in at a rate of 40 litres per minute. Inflow continues at 40 litres per minute for two minutes before tapering off uniformly to zero over the subsequent period of three minutes. Immediately this flow stops, 20 litres of water are added to the bath: this last amount is added at a steady rate and takes exactly one minute. If no more water is added:

a. How much water does the bathtub hold at the end of the fourth minute?

b. How much water remains in the bathtub at then end of the sixth minute?

c. When does the bathtub become empty?

Calculate your answer in the first instance using the graphical integration method. In the second instance build a system dynamics model using Powersim™ Studio. Use this model to confirm the answers you obtained through graphical integration.