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