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

	Scenario 1		Scenario 2
Container type	Container Q	Container R	Container Q	Container R
Volume of the container	5 u	6 u - 6	6 p	2 p x 3 = 6 p

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

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

Make u the same.

(1) x 6
30 u = 36 p --- (3)

(2) x 5
30 u = 30 p + 30 --- (4)

(3) = (4)
36 p = 30 p + 30
36 p - 30 p = 30
6 p = 30
1 p = 30 ÷ 6 = 5

Volume of Container R
= 6 p
= 6 x 5
= 30 ℓ

Answer(s): 30 ℓ