Gavin has 2 tanks. Tank J and Tank K are of different capacities. If Tank J is filled by a tap at a rate of 3 litres per minute and Tank K is filled by a tap at a rate of 7 litres per minute, when Tank J is completely filled, 6 litres of water flowed out from Tank K. If Tank J is filled by a tap at a rate of 6 litres per minute and Tank K is filled by a tap at a rate of 3 litres per minute, when Tank J is completely filled, Tank K is only one-quarter-filled. What is the capacity of Tank K? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank J |
Tank K |
Tank J |
Tank K |
Volume of the tank |
3 u |
7 u - 6 |
6 p |
3 p x 4 = 12 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 = 12 p
7 u = 12 p + 6 --- (2)
Make u the same.
(1) x 7
21 u = 42 p --- (3)
(2) x 3
21 u = 36 p + 18 --- (4)
(3) = (4)
42 p = 36 p + 18
42 p - 36 p = 18
6 p = 18
1 p = 18 ÷ 6 = 3
Volume of Tank K
= 12 p
= 12 x 3
= 36 ℓ
Answer(s): 36 ℓ