Mia has 2 containers. Container Y and Container Z are of different capacities. If Container Y is filled by a tap at a rate of 3 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, 7 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 4 litres per minute, when Container Y is completely filled, Container Z is only one-third-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	3 u	7 u - 7	6 p	4 p x 3 = 12 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)
7 u - 7 = 12 p
7 u = 12 p + 7 --- (2)

Make u the same.

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

(2) x 3
21 u = 36 p + 21 --- (4)

(3) = (4)
42 p = 36 p + 21
42 p - 36 p = 21
6 p = 21
1 p = 21 ÷ 6 = 3.5

Volume of Container Z
= 12 p
= 12 x 3.5
= 42 ℓ

Answer(s): 42 ℓ