Riordan has 2 containers. Container Y and Container Z are of different capacities. If Container Y is filled by a tap at a rate of 3 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 6 litres per minute and Container Z is filled by a tap at a rate of 5 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 |
3 u |
7 u - 8 |
6 p |
5 p x 2 = 10 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)
7 u - 8 = 10 p
7 u = 10 p + 8 --- (2)
Make u the same.
(1) x 7
21 u = 42 p --- (3)
(2) x 3
21 u = 30 p + 24 --- (4)
(3) = (4)
42 p = 30 p + 24
42 p - 30 p = 24
12 p = 24
1 p = 24 ÷ 12 = 2
Volume of Container Z
= 10 p
= 10 x 2
= 20 ℓ
Answer(s): 20 ℓ