Aubrey has 2 containers. Container Y and Container Z are of different capacities. If Container Y is filled by a tap at a rate of 5 litres per minute and Container Z is filled by a tap at a rate of 7 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 5 litres per minute and Container Z is filled by a tap at a rate of 3 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 |
5 u |
7 u - 8 |
5 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.
5 u = 5 p --- (1)
7 u - 8 = 6 p
7 u = 6 p + 8 --- (2)
Make u the same.
(1) x 7
35 u = 35 p --- (3)
(2) x 5
35 u = 30 p + 40 --- (4)
(3) = (4)
35 p = 30 p + 40
35 p - 30 p = 40
5 p = 40
1 p = 40 ÷ 5 = 8
Volume of Container Z
= 6 p
= 6 x 8
= 48 ℓ
Answer(s): 48 ℓ