Jamie has 2 containers. Container L and Container M are of different capacities. If Container L is filled by a tap at a rate of 3 litres per minute and Container M is filled by a tap at a rate of 5 litres per minute, when Container L is completely filled, 5 litres of water flowed out from Container M. If Container L is filled by a tap at a rate of 6 litres per minute and Container M is filled by a tap at a rate of 3 litres per minute, when Container L is completely filled, Container M is only one-third-filled. What is the capacity of Container M? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container L	Container M	Container L	Container M
Volume of the container	3 u	5 u - 5	6 p	3 p x 3 = 9 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)
5 u - 5 = 9 p
5 u = 9 p + 5 --- (2)

Make u the same.

(1) x 5
15 u = 30 p --- (3)

(2) x 3
15 u = 27 p + 15 --- (4)

(3) = (4)
30 p = 27 p + 15
30 p - 27 p = 15
3 p = 15
1 p = 15 ÷ 3 = 5

Volume of Container M
= 9 p
= 9 x 5
= 45 ℓ

Answer(s): 45 ℓ