Christian has 2 containers. Container D and Container E are of different capacities. If Container D is filled by a tap at a rate of 3 litres per minute and Container E is filled by a tap at a rate of 5 litres per minute, when Container D is completely filled, 7 litres of water flowed out from Container E. If Container D is filled by a tap at a rate of 6 litres per minute and Container E is filled by a tap at a rate of 4 litres per minute, when Container D is completely filled, Container E is only half-filled. What is the capacity of Container E? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container D	Container E	Container D	Container E
Volume of the container	3 u	5 u - 7	6 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 = 6 p --- (1)
5 u - 7 = 8 p
5 u = 8 p + 7 --- (2)

Make u the same.

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

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

(3) = (4)
30 p = 24 p + 21
30 p - 24 p = 21
6 p = 21
1 p = 21 ÷ 6 = 3.5

Volume of Container E
= 8 p
= 8 x 3.5
= 28 ℓ

Answer(s): 28 ℓ