Dylan has 2 tanks. Tank G and Tank H are of different capacities. If Tank G is filled by a tap at a rate of 3 litres per minute and Tank H is filled by a tap at a rate of 5 litres per minute, when Tank G is completely filled, 6 litres of water flowed out from Tank H. If Tank G is filled by a tap at a rate of 6 litres per minute and Tank H is filled by a tap at a rate of 2 litres per minute, when Tank G is completely filled, Tank H is only half-filled. What is the capacity of Tank H? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank G |
Tank H |
Tank G |
Tank H |
Volume of the tank |
3 u |
5 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)
5 u - 6 = 4 p
5 u = 4 p + 6 --- (2)
Make u the same.
(1) x 5
15 u = 30 p --- (3)
(2) x 3
15 u = 12 p + 18 --- (4)
(3) = (4)
30 p = 12 p + 18
30 p - 12 p = 18
18 p = 18
1 p = 18 ÷ 18 = 1
Volume of Tank H
= 4 p
= 4 x 1
= 4 ℓ
Answer(s): 4 ℓ