Lucas has 2 containers. Container Y and Container Z are of different capacities. If Container Y is filled by a tap at a rate of 4 litres per minute and Container Z is filled by a tap at a rate of 7 litres per minute, when Container Y is completely filled, 8 litres of water flowed out from Container Z. If Container Y is filled by a tap at a rate of 6 litres per minute and Container Z is filled by a tap at a rate of 2 litres per minute, when Container Y is completely filled, Container Z is only one-quarter-filled. What is the capacity of Container Z? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container Y	Container Z	Container Y	Container Z
Volume of the container	4 u	7 u - 8	6 p	2 p x 4 = 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)
7 u - 8 = 8 p
7 u = 8 p + 8 --- (2)

Make u the same.

(1) x 7
28 u = 42 p --- (3)

(2) x 4
28 u = 32 p + 32 --- (4)

(3) = (4)
42 p = 32 p + 32
42 p - 32 p = 32
10 p = 32
1 p = 32 ÷ 10 = 3.2

Volume of Container Z
= 8 p
= 8 x 3.2
= 25.6 ℓ

Answer(s): 25.6 ℓ