Hazel has 2 containers. Container Y and Container Z are of different capacities. If Container Y is filled by a tap at a rate of 4 litres per minute and Container Z is filled by a tap at a rate of 6 litres per minute, when Container Y is completely filled, 8 litres of water flowed out from Container Z. If Container Y is filled by a tap at a rate of 6 litres per minute and Container Z is filled by a tap at a rate of 4 litres per minute, when Container Y is completely filled, Container Z is only half-filled. What is the capacity of Container Z? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container Y |
Container Z |
Container Y |
Container Z |
Volume of the container |
4 u |
6 u - 8 |
6 p |
4 p x 2 = 8 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)
6 u - 8 = 8 p
6 u = 8 p + 8 --- (2)
Make u the same.
(1) x 3
12 u = 18 p --- (3)
(2) x 2
12 u = 16 p + 16 --- (4)
(3) = (4)
18 p = 16 p + 16
18 p - 16 p = 16
2 p = 16
1 p = 16 ÷ 2 = 8
Volume of Container Z
= 8 p
= 8 x 8
= 64 ℓ
Answer(s): 64 ℓ