Julian has 2 containers. Container B and Container C are of different capacities. If Container B is filled by a tap at a rate of 3 litres per minute and Container C is filled by a tap at a rate of 7 litres per minute, when Container B is completely filled, 5 litres of water flowed out from Container C. If Container B is filled by a tap at a rate of 4 litres per minute and Container C is filled by a tap at a rate of 2 litres per minute, when Container B is completely filled, Container C is only one-third-filled. What is the capacity of Container C? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container B |
Container C |
Container B |
Container C |
Volume of the container |
3 u |
7 u - 5 |
4 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.
3 u = 4 p --- (1)
7 u - 5 = 6 p
7 u = 6 p + 5 --- (2)
Make u the same.
(1) x 7
21 u = 28 p --- (3)
(2) x 3
21 u = 18 p + 15 --- (4)
(3) = (4)
28 p = 18 p + 15
28 p - 18 p = 15
10 p = 15
1 p = 15 ÷ 10 = 1.5
Volume of Container C
= 6 p
= 6 x 1.5
= 9 ℓ
Answer(s): 9 ℓ