Samuel 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 7 litres per minute, when Container Y is completely filled, 7 litres of water flowed out from Container Z. 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 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 |
4 u |
7 u - 7 |
4 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.
4 u = 4 p --- (1)
7 u - 7 = 6 p
7 u = 6 p + 7 --- (2)
Make u the same.
(1) x 7
28 u = 28 p --- (3)
(2) x 4
28 u = 24 p + 28 --- (4)
(3) = (4)
28 p = 24 p + 28
28 p - 24 p = 28
4 p = 28
1 p = 28 ÷ 4 = 7
Volume of Container Z
= 6 p
= 6 x 7
= 42 ℓ
Answer(s): 42 ℓ