Anthony has 2 containers. Container T and Container U are of different capacities. If Container T is filled by a tap at a rate of 4 litres per minute and Container U is filled by a tap at a rate of 5 litres per minute, when Container T is completely filled, 6 litres of water flowed out from Container U. If Container T is filled by a tap at a rate of 6 litres per minute and Container U is filled by a tap at a rate of 2 litres per minute, when Container T is completely filled, Container U is only one-third-filled. What is the capacity of Container U? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container T |
Container U |
Container T |
Container U |
Volume of the container |
4 u |
5 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.
4 u = 6 p --- (1)
5 u - 6 = 6 p
5 u = 6 p + 6 --- (2)
Make u the same.
(1) x 5
20 u = 30 p --- (3)
(2) x 4
20 u = 24 p + 24 --- (4)
(3) = (4)
30 p = 24 p + 24
30 p - 24 p = 24
6 p = 24
1 p = 24 ÷ 6 = 4
Volume of Container U
= 6 p
= 6 x 4
= 24 ℓ
Answer(s): 24 ℓ