Roshel has 2 tanks. Tank F and Tank G are of different capacities. If Tank F is filled by a tap at a rate of 4 litres per minute and Tank G is filled by a tap at a rate of 6 litres per minute, when Tank F is completely filled, 6 litres of water flowed out from Tank G. If Tank F is filled by a tap at a rate of 6 litres per minute and Tank G is filled by a tap at a rate of 2 litres per minute, when Tank F is completely filled, Tank G is only half-filled. What is the capacity of Tank G? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank F |
Tank G |
Tank F |
Tank G |
Volume of the tank |
4 u |
6 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.
4 u = 6 p --- (1)
6 u - 6 = 4 p
6 u = 4 p + 6 --- (2)
Make u the same.
(1) x 3
12 u = 18 p --- (3)
(2) x 2
12 u = 8 p + 12 --- (4)
(3) = (4)
18 p = 8 p + 12
18 p - 8 p = 12
10 p = 12
1 p = 12 ÷ 10 = 1.2
Volume of Tank G
= 4 p
= 4 x 1.2
= 4.8 ℓ
Answer(s): 4.8 ℓ