Josiah has 2 tanks. Tank U and Tank V are of different capacities. If Tank U is filled by a tap at a rate of 3 litres per minute and Tank V is filled by a tap at a rate of 7 litres per minute, when Tank U is completely filled, 5 litres of water flowed out from Tank V. If Tank U is filled by a tap at a rate of 6 litres per minute and Tank V is filled by a tap at a rate of 3 litres per minute, when Tank U is completely filled, Tank V is only one-third-filled. What is the capacity of Tank V? Express your answer in litres.

	Scenario 1		Scenario 2
Tank type	Tank U	Tank V	Tank U	Tank V
Volume of the tank	3 u	7 u - 5	6 p	3 p x 3 = 9 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)
7 u - 5 = 9 p
7 u = 9 p + 5 --- (2)

Make u the same.

(1) x 7
21 u = 42 p --- (3)

(2) x 3
21 u = 27 p + 15 --- (4)

(3) = (4)
42 p = 27 p + 15
42 p - 27 p = 15
15 p = 15
1 p = 15 ÷ 15 = 1

Volume of Tank V
= 9 p
= 9 x 1
= 9 ℓ

Answer(s): 9 ℓ