Tommy has 2 containers. Container C and Container D are of different capacities. If Container C is filled by a tap at a rate of 4 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, 6 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 4 litres per minute, when Container C is completely filled, Container D is only half-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 |
4 u |
7 u - 6 |
6 p |
4 p x 2 = 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)
7 u - 6 = 8 p
7 u = 8 p + 6 --- (2)
Make u the same.
(1) x 7
28 u = 42 p --- (3)
(2) x 4
28 u = 32 p + 24 --- (4)
(3) = (4)
42 p = 32 p + 24
42 p - 32 p = 24
10 p = 24
1 p = 24 ÷ 10 = 2.4
Volume of Container D
= 8 p
= 8 x 2.4
= 19.2 ℓ
Answer(s): 19.2 ℓ