John 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, 5 litres of water flowed out from Tank N. 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 3 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 - 5 |
5 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.
5 u = 5 p --- (1)
7 u - 5 = 6 p
7 u = 6 p + 5 --- (2)
Make u the same.
(1) x 7
35 u = 35 p --- (3)
(2) x 5
35 u = 30 p + 25 --- (4)
(3) = (4)
35 p = 30 p + 25
35 p - 30 p = 25
5 p = 25
1 p = 25 ÷ 5 = 5
Volume of Tank N
= 6 p
= 6 x 5
= 30 ℓ
Answer(s): 30 ℓ