Aubrey has 2 containers. Container X and Container Y are of different capacities. If Container X is filled by a tap at a rate of 3 litres per minute and Container Y is filled by a tap at a rate of 5 litres per minute, when Container X is completely filled, 6 litres of water flowed out from Container Y. If Container X is filled by a tap at a rate of 6 litres per minute and Container Y is filled by a tap at a rate of 2 litres per minute, when Container X is completely filled, Container Y is only half-filled. What is the capacity of Container Y? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container X	Container Y	Container X	Container Y
Volume of the container	3 u	5 u - 6	6 p	2 p x 2 = 4 p

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

3 u = 6 p --- (1)
5 u - 6 = 4 p
5 u = 4 p + 6 --- (2)

Make u the same.

(1) x 5
15 u = 30 p --- (3)

(2) x 3
15 u = 12 p + 18 --- (4)

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

Volume of Container Y
= 4 p
= 4 x 1
= 4 ℓ

Answer(s): 4 ℓ