Julian has 2 containers. Container T and Container U are of different capacities. If Container T is filled by a tap at a rate of 4 litres per minute and Container U is filled by a tap at a rate of 6 litres per minute, when Container T is completely filled, 8 litres of water flowed out from Container U. If Container T is filled by a tap at a rate of 6 litres per minute and Container U is filled by a tap at a rate of 4 litres per minute, when Container T is completely filled, Container U is only half-filled. What is the capacity of Container U? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container T	Container U	Container T	Container U
Volume of the container	4 u	6 u - 8	6 p	4 p x 2 = 8 p

Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.

4 u = 6 p --- (1)
6 u - 8 = 8 p
6 u = 8 p + 8 --- (2)

Make u the same.

(1) x 3
12 u = 18 p --- (3)

(2) x 2
12 u = 16 p + 16 --- (4)

(3) = (4)
18 p = 16 p + 16
18 p - 16 p = 16
2 p = 16
1 p = 16 ÷ 2 = 8

Volume of Container U
= 8 p
= 8 x 8
= 64 ℓ

Answer(s): 64 ℓ