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

	Scenario 1		Scenario 2
Container type	Container P	Container Q	Container P	Container Q
Volume of the container	3 u	5 u - 7	5 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.

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

Make u the same.

(1) x 5
15 u = 25 p --- (3)

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

(3) = (4)
25 p = 18 p + 21
25 p - 18 p = 21
7 p = 21
1 p = 21 ÷ 7 = 3

Volume of Container Q
= 6 p
= 6 x 3
= 18 ℓ

Answer(s): 18 ℓ