Emma has 2 containers. Container M and Container N are of different capacities. If Container M is filled by a tap at a rate of 5 litres per minute and Container N is filled by a tap at a rate of 6 litres per minute, when Container M is completely filled, 8 litres of water flowed out from Container N. If Container M is filled by a tap at a rate of 5 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	5 u	6 u - 8	5 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.

5 u = 5 p --- (1)
6 u - 8 = 4 p
6 u = 4 p + 8 --- (2)

Make u the same.

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

(2) x 5
30 u = 20 p + 40 --- (4)

(3) = (4)
30 p = 20 p + 40
30 p - 20 p = 40
10 p = 40
1 p = 40 ÷ 10 = 4

Volume of Container N
= 4 p
= 4 x 4
= 16 ℓ

Answer(s): 16 ℓ