2026 NASS P2 Q6

An empty water tank has a capacity of \(4.8\text{ m}^3\).

An inlet pipe pumps water into the tank at a constant rate of \(x\text{ cm}^3/\text{s}\).

On a particular day, the tank took 1 hour 40 minutes longer than usual to fill because of a crack at the bottom of the tank.

Water leaked through the crack at a constant rate of \(1500\text{ cm}^3/\text{s}\).

1. Show that \(x^2-1500x-1200000=0\).[4]
2. Solve the equation \(x^2-1500x-1200000=0\).
   Give your solutions correct to two decimal places.[3]
3. Hence calculate the time taken to fill the tank on that day.
   Give your answer in hours and minutes, correct to the nearest minute.[2]
4. The water tank is in the shape of an inverted cone with a height of 200 cm.
   On the axes, sketch a graph to show the relationship between the height of the water, \(h\text{ cm}\), and the time, \(t\) hours, as the tank was filled that day.[1]