Sophia has 2 containers. Container W and Container X are of different capacities. If Container W is filled by a tap at a rate of 3 litres per minute and Container X is filled by a tap at a rate of 7 litres per minute, when Container W is completely filled, 7 litres of water flowed out from Container X. If Container W is filled by a tap at a rate of 4 litres per minute and Container X is filled by a tap at a rate of 4 litres per minute, when Container W is completely filled, Container X is only half-filled. What is the capacity of Container X? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container W	Container X	Container W	Container X
Volume of the container	3 u	7 u - 7	4 p	4 p x 2 = 8 p

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

3 u = 4 p --- (1)
7 u - 7 = 8 p
7 u = 8 p + 7 --- (2)

Make u the same.

(1) x 7
21 u = 28 p --- (3)

(2) x 3
21 u = 24 p + 21 --- (4)

(3) = (4)
28 p = 24 p + 21
28 p - 24 p = 21
4 p = 21
1 p = 21 ÷ 4 = 5.25

Volume of Container X
= 8 p
= 8 x 5.25
= 42 ℓ

Answer(s): 42 ℓ