Zoe has 2 tanks. Tank H and Tank J are of different capacities. If Tank H is filled by a tap at a rate of 4 litres per minute and Tank J is filled by a tap at a rate of 5 litres per minute, when Tank H is completely filled, 6 litres of water flowed out from Tank J. If Tank H is filled by a tap at a rate of 6 litres per minute and Tank J is filled by a tap at a rate of 3 litres per minute, when Tank H is completely filled, Tank J is only half-filled. What is the capacity of Tank J? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank H |
Tank J |
Tank H |
Tank J |
Volume of the tank |
4 u |
5 u - 6 |
6 p |
3 p x 2 = 6 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)
5 u - 6 = 6 p
5 u = 6 p + 6 --- (2)
Make u the same.
(1) x 5
20 u = 30 p --- (3)
(2) x 4
20 u = 24 p + 24 --- (4)
(3) = (4)
30 p = 24 p + 24
30 p - 24 p = 24
6 p = 24
1 p = 24 ÷ 6 = 4
Volume of Tank J
= 6 p
= 6 x 4
= 24 ℓ
Answer(s): 24 ℓ