Joseph has 2 containers. Container E and Container F are of different capacities. If Container E is filled by a tap at a rate of 4 litres per minute and Container F is filled by a tap at a rate of 7 litres per minute, when Container E is completely filled, 7 litres of water flowed out from Container F. If Container E is filled by a tap at a rate of 6 litres per minute and Container F is filled by a tap at a rate of 2 litres per minute, when Container E is completely filled, Container F is only one-quarter-filled. What is the capacity of Container F? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container E |
Container F |
Container E |
Container F |
Volume of the container |
4 u |
7 u - 7 |
6 p |
2 p x 4 = 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 - 7 = 8 p
7 u = 8 p + 7 --- (2)
Make u the same.
(1) x 7
28 u = 42 p --- (3)
(2) x 4
28 u = 32 p + 28 --- (4)
(3) = (4)
42 p = 32 p + 28
42 p - 32 p = 28
10 p = 28
1 p = 28 ÷ 10 = 2.8
Volume of Container F
= 8 p
= 8 x 2.8
= 22.4 ℓ
Answer(s): 22.4 ℓ