Christian has 2 containers. Container U and Container V are of different capacities. If Container U is filled by a tap at a rate of 4 litres per minute and Container V is filled by a tap at a rate of 6 litres per minute, when Container U is completely filled, 6 litres of water flowed out from Container V. If Container U is filled by a tap at a rate of 6 litres per minute and Container V is filled by a tap at a rate of 3 litres per minute, when Container U is completely filled, Container V is only half-filled. What is the capacity of Container V? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container U	Container V	Container U	Container V
Volume of the container	4 u	6 u - 6	6 p	3 p x 2 = 6 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 - 6 = 6 p
6 u = 6 p + 6 --- (2)

Make u the same.

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

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

(3) = (4)
18 p = 12 p + 12
18 p - 12 p = 12
6 p = 12
1 p = 12 ÷ 6 = 2

Volume of Container V
= 6 p
= 6 x 2
= 12 ℓ

Answer(s): 12 ℓ