Isabella has 2 tanks. Tank P and Tank Q are of different capacities. If Tank P is filled by a tap at a rate of 4 litres per minute and Tank Q is filled by a tap at a rate of 6 litres per minute, when Tank P is completely filled, 5 litres of water flowed out from Tank Q. If Tank P is filled by a tap at a rate of 6 litres per minute and Tank Q is filled by a tap at a rate of 2 litres per minute, when Tank P is completely filled, Tank Q is only half-filled. What is the capacity of Tank Q? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank P |
Tank Q |
Tank P |
Tank Q |
Volume of the tank |
4 u |
6 u - 5 |
6 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.
4 u = 6 p --- (1)
6 u - 5 = 4 p
6 u = 4 p + 5 --- (2)
Make u the same.
(1) x 3
12 u = 18 p --- (3)
(2) x 2
12 u = 8 p + 10 --- (4)
(3) = (4)
18 p = 8 p + 10
18 p - 8 p = 10
10 p = 10
1 p = 10 ÷ 10 = 1
Volume of Tank Q
= 4 p
= 4 x 1
= 4 ℓ
Answer(s): 4 ℓ