Alexander has 2 tanks. Tank M and Tank N are of different capacities. If Tank M is filled by a tap at a rate of 5 litres per minute and Tank N is filled by a tap at a rate of 7 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 4 litres per minute and Tank N is filled by a tap at a rate of 2 litres per minute, when Tank M is completely filled, Tank N is only half-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 |
5 u |
7 u - 6 |
4 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.
5 u = 4 p --- (1)
7 u - 6 = 4 p
7 u = 4 p + 6 --- (2)
Make u the same.
(1) x 7
35 u = 28 p --- (3)
(2) x 5
35 u = 20 p + 30 --- (4)
(3) = (4)
28 p = 20 p + 30
28 p - 20 p = 30
8 p = 30
1 p = 30 ÷ 8 = 3.75
Volume of Tank N
= 4 p
= 4 x 3.75
= 15 ℓ
Answer(s): 15 ℓ