Caleb has 2 containers. Container Q and Container R are of different capacities. If Container Q is filled by a tap at a rate of 5 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, 6 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-third-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 |
5 u |
6 u - 6 |
6 p |
2 p x 3 = 6 p |
Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.
5 u = 6 p --- (1)
6 u - 6 = 6 p
6 u = 6 p + 6 --- (2)
Make u the same.
(1) x 6
30 u = 36 p --- (3)
(2) x 5
30 u = 30 p + 30 --- (4)
(3) = (4)
36 p = 30 p + 30
36 p - 30 p = 30
6 p = 30
1 p = 30 ÷ 6 = 5
Volume of Container R
= 6 p
= 6 x 5
= 30 ℓ
Answer(s): 30 ℓ