Elizabeth has 2 containers. Container Z and Container A are of different capacities. If Container Z is filled by a tap at a rate of 3 litres per minute and Container A is filled by a tap at a rate of 5 litres per minute, when Container Z is completely filled, 5 litres of water flowed out from Container A. If Container Z is filled by a tap at a rate of 6 litres per minute and Container A is filled by a tap at a rate of 4 litres per minute, when Container Z is completely filled, Container A is only half-filled. What is the capacity of Container A? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container Z |
Container A |
Container Z |
Container A |
Volume of the container |
3 u |
5 u - 5 |
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.
3 u = 6 p --- (1)
5 u - 5 = 8 p
5 u = 8 p + 5 --- (2)
Make u the same.
(1) x 5
15 u = 30 p --- (3)
(2) x 3
15 u = 24 p + 15 --- (4)
(3) = (4)
30 p = 24 p + 15
30 p - 24 p = 15
6 p = 15
1 p = 15 ÷ 6 = 2.5
Volume of Container A
= 8 p
= 8 x 2.5
= 20 ℓ
Answer(s): 20 ℓ