Michael has 2 tanks. Tank N and Tank P are of different capacities. If Tank N is filled by a tap at a rate of 3 litres per minute and Tank P is filled by a tap at a rate of 5 litres per minute, when Tank N is completely filled, 8 litres of water flowed out from Tank P. If Tank N is filled by a tap at a rate of 6 litres per minute and Tank P is filled by a tap at a rate of 3 litres per minute, when Tank N is completely filled, Tank P is only one-third-filled. What is the capacity of Tank P? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank N |
Tank P |
Tank N |
Tank P |
Volume of the tank |
3 u |
5 u - 8 |
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 - 8 = 9 p
5 u = 9 p + 8 --- (2)
Make u the same.
(1) x 5
15 u = 30 p --- (3)
(2) x 3
15 u = 27 p + 24 --- (4)
(3) = (4)
30 p = 27 p + 24
30 p - 27 p = 24
3 p = 24
1 p = 24 ÷ 3 = 8
Volume of Tank P
= 9 p
= 9 x 8
= 72 ℓ
Answer(s): 72 ℓ