Victoria has 2 containers. Container H and Container J are of different capacities. If Container H is filled by a tap at a rate of 4 litres per minute and Container J is filled by a tap at a rate of 7 litres per minute, when Container H is completely filled, 5 litres of water flowed out from Container J. If Container H is filled by a tap at a rate of 3 litres per minute and Container J is filled by a tap at a rate of 2 litres per minute, when Container H is completely filled, Container J is only half-filled. What is the capacity of Container J? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container H |
Container J |
Container H |
Container J |
Volume of the container |
4 u |
7 u - 5 |
3 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 = 3 p --- (1)
7 u - 5 = 4 p
7 u = 4 p + 5 --- (2)
Make u the same.
(1) x 7
28 u = 21 p --- (3)
(2) x 4
28 u = 16 p + 20 --- (4)
(3) = (4)
21 p = 16 p + 20
21 p - 16 p = 20
5 p = 20
1 p = 20 ÷ 5 = 4
Volume of Container J
= 4 p
= 4 x 4
= 16 ℓ
Answer(s): 16 ℓ