Ethan has 2 tanks. Tank T and Tank U are of different capacities. If Tank T is filled by a tap at a rate of 5 litres per minute and Tank U is filled by a tap at a rate of 6 litres per minute, when Tank T is completely filled, 6 litres of water flowed out from Tank U. If Tank T is filled by a tap at a rate of 4 litres per minute and Tank U is filled by a tap at a rate of 2 litres per minute, when Tank T is completely filled, Tank U is only half-filled. What is the capacity of Tank U? Express your answer in litres.

	Scenario 1		Scenario 2
Tank type	Tank T	Tank U	Tank T	Tank U
Volume of the tank	5 u	6 u - 6	4 p	2 p x 2 = 4 p

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

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

Make u the same.

(1) x 6
30 u = 24 p --- (3)

(2) x 5
30 u = 20 p + 30 --- (4)

(3) = (4)
24 p = 20 p + 30
24 p - 20 p = 30
4 p = 30
1 p = 30 ÷ 4 = 7.5

Volume of Tank U
= 4 p
= 4 x 7.5
= 30 ℓ

Answer(s): 30 ℓ