Josiah has 2 tanks. Tank N and Tank P are of different capacities. If Tank N is filled by a tap at a rate of 4 litres per minute and Tank P is filled by a tap at a rate of 6 litres per minute, when Tank N is completely filled, 6 litres of water flowed out from Tank P. If Tank N is filled by a tap at a rate of 6 litres per minute and Tank P is filled by a tap at a rate of 4 litres per minute, when Tank N is completely filled, Tank P is only half-filled. What is the capacity of Tank P? Express your answer in litres.

	Scenario 1		Scenario 2
Tank type	Tank N	Tank P	Tank N	Tank P
Volume of the tank	4 u	6 u - 6	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.

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

Make u the same.

(1) x 3
12 u = 18 p --- (3)

(2) x 2
12 u = 16 p + 12 --- (4)

(3) = (4)
18 p = 16 p + 12
18 p - 16 p = 12
2 p = 12
1 p = 12 ÷ 2 = 6

Volume of Tank P
= 8 p
= 8 x 6
= 48 ℓ

Answer(s): 48 ℓ