Natalie has 2 tanks. Tank B and Tank C are of different capacities. If Tank B is filled by a tap at a rate of 3 litres per minute and Tank C is filled by a tap at a rate of 7 litres per minute, when Tank B is completely filled, 5 litres of water flowed out from Tank C. If Tank B is filled by a tap at a rate of 6 litres per minute and Tank C is filled by a tap at a rate of 4 litres per minute, when Tank B is completely filled, Tank C is only one-third-filled. What is the capacity of Tank C? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank B |
Tank C |
Tank B |
Tank C |
Volume of the tank |
3 u |
7 u - 5 |
6 p |
4 p x 3 = 12 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)
7 u - 5 = 12 p
7 u = 12 p + 5 --- (2)
Make u the same.
(1) x 7
21 u = 42 p --- (3)
(2) x 3
21 u = 36 p + 15 --- (4)
(3) = (4)
42 p = 36 p + 15
42 p - 36 p = 15
6 p = 15
1 p = 15 ÷ 6 = 2.5
Volume of Tank C
= 12 p
= 12 x 2.5
= 30 ℓ
Answer(s): 30 ℓ