Michael has 2 containers. Container Q and Container R are of different capacities. If Container Q is filled by a tap at a rate of 4 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, 7 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 half-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	4 u	6 u - 7	6 p	2 p x 2 = 4 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)
6 u - 7 = 4 p
6 u = 4 p + 7 --- (2)

Make u the same.

(1) x 3
12 u = 18 p --- (3)

(2) x 2
12 u = 8 p + 14 --- (4)

(3) = (4)
18 p = 8 p + 14
18 p - 8 p = 14
10 p = 14
1 p = 14 ÷ 10 = 1.4

Volume of Container R
= 4 p
= 4 x 1.4
= 5.6 ℓ

Answer(s): 5.6 ℓ