A rectangular water tank measures 2.5m long, 2.4m wide and 2.1m high. The tank contained some water up to a height of 1.21m.An inlet pipe was opened and water let to flow into the tank at a rate of 8 litres per minute. After one hour, a drain pipe was opened and water allowed to flow out of the tank at a rate of 6 litres per minute.Calculatei. The height of water in tank after 3 hours.ii. The total time taken to fill up the tank.

i. The height of water in the tank after 3 hours:

First, we need to calculate the volume of water that flowed into the tank in the first hour. The rate of flow is 8 litres per minute, so in one hour (60 minutes), the volume of water that flowed into the tank is 8 litres/minute * 60 minutes = 480 litres.

Since 1 cubic meter (m^3) is equal to 1000 litres, the volume of water that flowed into the tank in the first hour is 480 litres * 1 m^3/1000 litres = 0.48 m^3.

Next, we need to calculate the volume of water that flowed into and out of the tank in the next two hours. The rate of flow into the tank is 8 litres per minute and the rate of flow out of the tank is 6 litres per minute, so the net rate of flow into the tank is 8 litres/minute - 6 litres/minute = 2 litres/minute.

In two hours (120 minutes), the volume of water that flowed into the tank is 2 litres/minute * 120 minutes = 240 litres = 0.24 m^3.

So, the total volume of water in the tank after 3 hours is the initial volume of water plus the volume of water that flowed into the tank in the first hour plus the volume of water that flowed into the tank in the next two hours.

The initial volume of water is the area of the base of the tank times the initial height of the water. The area of the base of the tank is its length times its width, so the initial volume of water is 2.5m * 2.4m * 1.21m = 7.26 m^3.

Therefore, the total volume of water in the tank after 3 hours is 7.26 m^3 + 0.48 m^3 + 0.24 m^3 = 7.98 m^3.

Finally, we need to calculate the height of the water in the tank after 3 hours. The volume of a rectangular prism is its length times its width times its height, so the height of the water is its volume divided by the area of the base of the tank.

Therefore, the height of the water in the tank after 3 hours is 7.98 m^3 / (2.5m * 2.4m) = 1.33 m.

ii. The total time taken to fill up the tank:

First, we need to calculate the volume of the tank. The volume of a rectangular prism is its length times its width times its height, so the volume of the tank is 2.5m * 2.4m * 2.1m = 12.6 m^3.

Next, we need to calculate the volume of water needed to fill up the tank. The volume of water needed is the volume of the tank minus the volume of water in the tank after 3 hours, which is 12.6 m^3 - 7.98 m^3 = 4.62 m^3.

Finally, we need to calculate the time taken to fill up the tank. The rate of flow into the tank is 2 litres per minute, so the time taken to fill up the tank is the volume of water needed divided by the rate of flow into the tank.

Therefore, the time taken to fill up the tank is 4.62 m^3 / (2 litres/minute * 1 m^3/1000 litres) = 2310 minutes = 38.5 hours.

Therefore, the total time taken to fill up the tank is the time taken to fill up the tank after 3 hours plus the 3 hours that have already passed, which is 38.5 hours + 3 hours = 41.5 hours.