Zoe has 2 containers. Container Z and Container A are of different capacities. If Container Z is filled by a tap at a rate of 3 litres per minute and Container A is filled by a tap at a rate of 7 litres per minute, when Container Z is completely filled, 6 litres of water flowed out from Container A. If Container Z is filled by a tap at a rate of 5 litres per minute and Container A is filled by a tap at a rate of 5 litres per minute, when Container Z is completely filled, Container A is only half-filled. What is the capacity of Container A? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container Z	Container A	Container Z	Container A
Volume of the container	3 u	7 u - 6	5 p	5 p x 2 = 10 p

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

3 u = 5 p --- (1)
7 u - 6 = 10 p
7 u = 10 p + 6 --- (2)

Make u the same.

(1) x 7
21 u = 35 p --- (3)

(2) x 3
21 u = 30 p + 18 --- (4)

(3) = (4)
35 p = 30 p + 18
35 p - 30 p = 18
5 p = 18
1 p = 18 ÷ 5 = 3.6

Volume of Container A
= 10 p
= 10 x 3.6
= 36 ℓ

Answer(s): 36 ℓ