John has 2 containers. Container Q and Container R are of different capacities. If Container Q is filled by a tap at a rate of 4 litres per minute and Container R is filled by a tap at a rate of 6 litres per minute, when Container Q is completely filled, 7 litres of water flowed out from Container R. If Container Q is filled by a tap at a rate of 6 litres per minute and Container R is filled by a tap at a rate of 2 litres per minute, when Container Q is completely filled, Container R is only one-quarter-filled. What is the capacity of Container R? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container Q |
Container R |
Container Q |
Container R |
Volume of the container |
4 u |
6 u - 7 |
6 p |
2 p x 4 = 8 p |
Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.
4 u = 6 p --- (1)
6 u - 7 = 8 p
6 u = 8 p + 7 --- (2)
Make u the same.
(1) x 3
12 u = 18 p --- (3)
(2) x 2
12 u = 16 p + 14 --- (4)
(3) = (4)
18 p = 16 p + 14
18 p - 16 p = 14
2 p = 14
1 p = 14 ÷ 2 = 7
Volume of Container R
= 8 p
= 8 x 7
= 56 ℓ
Answer(s): 56 ℓ