Wyatt 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, 8 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 4 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 |
3 u |
5 u - 8 |
6 p |
4 p x 2 = 8 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 - 8 = 8 p
5 u = 8 p + 8 --- (2)
Make u the same.
(1) x 5
15 u = 30 p --- (3)
(2) x 3
15 u = 24 p + 24 --- (4)
(3) = (4)
30 p = 24 p + 24
30 p - 24 p = 24
6 p = 24
1 p = 24 ÷ 6 = 4
Volume of Tank N
= 8 p
= 8 x 4
= 32 ℓ
Answer(s): 32 ℓ