Sebastian has 2 tanks. Tank S and Tank T are of different capacities. If Tank S is filled by a tap at a rate of 3 litres per minute and Tank T is filled by a tap at a rate of 7 litres per minute, when Tank S is completely filled, 6 litres of water flowed out from Tank T. If Tank S is filled by a tap at a rate of 6 litres per minute and Tank T is filled by a tap at a rate of 2 litres per minute, when Tank S is completely filled, Tank T is only half-filled. What is the capacity of Tank T? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank S |
Tank T |
Tank S |
Tank T |
Volume of the tank |
3 u |
7 u - 6 |
6 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.
3 u = 6 p --- (1)
7 u - 6 = 4 p
7 u = 4 p + 6 --- (2)
Make u the same.
(1) x 7
21 u = 42 p --- (3)
(2) x 3
21 u = 12 p + 18 --- (4)
(3) = (4)
42 p = 12 p + 18
42 p - 12 p = 18
30 p = 18
1 p = 18 ÷ 30 = 0.6
Volume of Tank T
= 4 p
= 4 x 0.6
= 2.4 ℓ
Answer(s): 2.4 ℓ