Alexander has 2 tanks. Tank Z and Tank A are of different capacities. If Tank Z is filled by a tap at a rate of 5 litres per minute and Tank A is filled by a tap at a rate of 6 litres per minute, when Tank Z is completely filled, 6 litres of water flowed out from Tank A. If Tank Z is filled by a tap at a rate of 6 litres per minute and Tank A is filled by a tap at a rate of 2 litres per minute, when Tank Z is completely filled, Tank A is only one-third-filled. What is the capacity of Tank A? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank Z |
Tank A |
Tank Z |
Tank A |
Volume of the tank |
5 u |
6 u - 6 |
6 p |
2 p x 3 = 6 p |
Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.
5 u = 6 p --- (1)
6 u - 6 = 6 p
6 u = 6 p + 6 --- (2)
Make u the same.
(1) x 6
30 u = 36 p --- (3)
(2) x 5
30 u = 30 p + 30 --- (4)
(3) = (4)
36 p = 30 p + 30
36 p - 30 p = 30
6 p = 30
1 p = 30 ÷ 6 = 5
Volume of Tank A
= 6 p
= 6 x 5
= 30 ℓ
Answer(s): 30 ℓ