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

	Scenario 1		Scenario 2
Tank type	Tank Q	Tank R	Tank Q	Tank R
Volume of the tank	3 u	7 u - 7	6 p	3 p x 4 = 12 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 - 7 = 12 p
7 u = 12 p + 7 --- (2)

Make u the same.

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

(2) x 3
21 u = 36 p + 21 --- (4)

(3) = (4)
42 p = 36 p + 21
42 p - 36 p = 21
6 p = 21
1 p = 21 ÷ 6 = 3.5

Volume of Tank R
= 12 p
= 12 x 3.5
= 42 ℓ

Answer(s): 42 ℓ