Jamie has 2 containers. Container F and Container G are of different capacities. If Container F is filled by a tap at a rate of 4 litres per minute and Container G is filled by a tap at a rate of 5 litres per minute, when Container F is completely filled, 8 litres of water flowed out from Container G. If Container F is filled by a tap at a rate of 4 litres per minute and Container G is filled by a tap at a rate of 2 litres per minute, when Container F is completely filled, Container G is only half-filled. What is the capacity of Container G? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container F |
Container G |
Container F |
Container G |
Volume of the container |
4 u |
5 u - 8 |
4 p |
2 p x 2 = 4 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)
5 u - 8 = 4 p
5 u = 4 p + 8 --- (2)
Make u the same.
(1) x 5
20 u = 20 p --- (3)
(2) x 4
20 u = 16 p + 32 --- (4)
(3) = (4)
20 p = 16 p + 32
20 p - 16 p = 32
4 p = 32
1 p = 32 ÷ 4 = 8
Volume of Container G
= 4 p
= 4 x 8
= 32 ℓ
Answer(s): 32 ℓ