Ryan has 2 tanks. Tank J and Tank K are of different capacities. If Tank J is filled by a tap at a rate of 4 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, 7 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 5 litres per minute, when Tank J is completely filled, Tank K is only half-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 |
4 u |
7 u - 7 |
6 p |
5 p x 2 = 10 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)
7 u - 7 = 10 p
7 u = 10 p + 7 --- (2)
Make u the same.
(1) x 7
28 u = 42 p --- (3)
(2) x 4
28 u = 40 p + 28 --- (4)
(3) = (4)
42 p = 40 p + 28
42 p - 40 p = 28
2 p = 28
1 p = 28 ÷ 2 = 14
Volume of Tank K
= 10 p
= 10 x 14
= 140 ℓ
Answer(s): 140 ℓ