Josiah 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 7 litres per minute, when Container D is completely filled, 5 litres of water flowed out from Container E. If Container D is filled by a tap at a rate of 5 litres per minute and Container E is filled by a tap at a rate of 2 litres per minute, when Container D is completely filled, Container E is only one-fifth-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	7 u - 5	5 p	2 p x 5 = 10 p

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

3 u = 5 p --- (1)
7 u - 5 = 10 p
7 u = 10 p + 5 --- (2)

Make u the same.

(1) x 7
21 u = 35 p --- (3)

(2) x 3
21 u = 30 p + 15 --- (4)

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

Volume of Container E
= 10 p
= 10 x 3
= 30 ℓ

Answer(s): 30 ℓ