Nora has 2 tanks. Tank C and Tank D are of different capacities. If Tank C is filled by a tap at a rate of 3 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, 5 litres of water flowed out from Tank D. 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 3 litres per minute, when Tank C is completely filled, Tank D is only half-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 |
3 u |
5 u - 5 |
4 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.
3 u = 4 p --- (1)
5 u - 5 = 6 p
5 u = 6 p + 5 --- (2)
Make u the same.
(1) x 5
15 u = 20 p --- (3)
(2) x 3
15 u = 18 p + 15 --- (4)
(3) = (4)
20 p = 18 p + 15
20 p - 18 p = 15
2 p = 15
1 p = 15 ÷ 2 = 7.5
Volume of Tank D
= 6 p
= 6 x 7.5
= 45 ℓ
Answer(s): 45 ℓ