Layla has 2 tanks. Tank M and Tank N are of different capacities. If Tank M is filled by a tap at a rate of 3 litres per minute and Tank N is filled by a tap at a rate of 5 litres per minute, when Tank M is completely filled, 6 litres of water flowed out from Tank N. If Tank M is filled by a tap at a rate of 6 litres per minute and Tank N is filled by a tap at a rate of 3 litres per minute, when Tank M is completely filled, Tank N is only one-third-filled. What is the capacity of Tank N? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank M |
Tank N |
Tank M |
Tank N |
Volume of the tank |
3 u |
5 u - 6 |
6 p |
3 p x 3 = 9 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 = 9 p
5 u = 9 p + 6 --- (2)
Make u the same.
(1) x 5
15 u = 30 p --- (3)
(2) x 3
15 u = 27 p + 18 --- (4)
(3) = (4)
30 p = 27 p + 18
30 p - 27 p = 18
3 p = 18
1 p = 18 ÷ 3 = 6
Volume of Tank N
= 9 p
= 9 x 6
= 54 ℓ
Answer(s): 54 ℓ