Luke has 2 containers. Container C and Container D are of different capacities. If Container C is filled by a tap at a rate of 3 litres per minute and Container D is filled by a tap at a rate of 7 litres per minute, when Container C is completely filled, 8 litres of water flowed out from Container D. If Container C is filled by a tap at a rate of 6 litres per minute and Container D is filled by a tap at a rate of 3 litres per minute, when Container C is completely filled, Container D is only one-quarter-filled. What is the capacity of Container D? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container C |
Container D |
Container C |
Container D |
Volume of the container |
3 u |
7 u - 8 |
6 p |
3 p x 4 = 12 p |
Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.
3 u = 6 p --- (1)
7 u - 8 = 12 p
7 u = 12 p + 8 --- (2)
Make u the same.
(1) x 7
21 u = 42 p --- (3)
(2) x 3
21 u = 36 p + 24 --- (4)
(3) = (4)
42 p = 36 p + 24
42 p - 36 p = 24
6 p = 24
1 p = 24 ÷ 6 = 4
Volume of Container D
= 12 p
= 12 x 4
= 48 ℓ
Answer(s): 48 ℓ