Matthew 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 7 litres per minute, when Container Z is completely filled, 7 litres of water flowed out from Container A. 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 3 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 |
7 u - 7 |
3 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.
3 u = 3 p --- (1)
7 u - 7 = 6 p
7 u = 6 p + 7 --- (2)
Make u the same.
(1) x 7
21 u = 21 p --- (3)
(2) x 3
21 u = 18 p + 21 --- (4)
(3) = (4)
21 p = 18 p + 21
21 p - 18 p = 21
3 p = 21
1 p = 21 ÷ 3 = 7
Volume of Container A
= 6 p
= 6 x 7
= 42 ℓ
Answer(s): 42 ℓ