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

	Scenario 1		Scenario 2
Container type	Container M	Container N	Container M	Container N
Volume of the container	3 u	7 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.

3 u = 6 p --- (1)
7 u - 7 = 4 p
7 u = 4 p + 7 --- (2)

Make u the same.

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

(2) x 3
21 u = 12 p + 21 --- (4)

(3) = (4)
42 p = 12 p + 21
42 p - 12 p = 21
30 p = 21
1 p = 21 ÷ 30 = 0.7

Volume of Container N
= 4 p
= 4 x 0.7
= 2.8 ℓ

Answer(s): 2.8 ℓ