Nora has 2 containers. Container D and Container E are of different capacities. If Container D is filled by a tap at a rate of 3 litres per minute and Container E is filled by a tap at a rate of 7 litres per minute, when Container D is completely filled, 8 litres of water flowed out from Container E. If Container D is filled by a tap at a rate of 4 litres per minute and Container E is filled by a tap at a rate of 2 litres per minute, when Container D is completely filled, Container E is only half-filled. What is the capacity of Container E? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container D |
Container E |
Container D |
Container E |
Volume of the container |
3 u |
7 u - 8 |
4 p |
2 p x 2 = 4 p |
Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.
3 u = 4 p --- (1)
7 u - 8 = 4 p
7 u = 4 p + 8 --- (2)
Make u the same.
(1) x 7
21 u = 28 p --- (3)
(2) x 3
21 u = 12 p + 24 --- (4)
(3) = (4)
28 p = 12 p + 24
28 p - 12 p = 24
16 p = 24
1 p = 24 ÷ 16 = 1.5
Volume of Container E
= 4 p
= 4 x 1.5
= 6 ℓ
Answer(s): 6 ℓ