Matthew has 2 containers. Container E and Container F are of different capacities. If Container E is filled by a tap at a rate of 3 litres per minute and Container F is filled by a tap at a rate of 5 litres per minute, when Container E is completely filled, 5 litres of water flowed out from Container F. If Container E is filled by a tap at a rate of 3 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 half-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 |
3 u |
5 u - 5 |
3 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 = 3 p --- (1)
5 u - 5 = 4 p
5 u = 4 p + 5 --- (2)
Make u the same.
(1) x 5
15 u = 15 p --- (3)
(2) x 3
15 u = 12 p + 15 --- (4)
(3) = (4)
15 p = 12 p + 15
15 p - 12 p = 15
3 p = 15
1 p = 15 ÷ 3 = 5
Volume of Container F
= 4 p
= 4 x 5
= 20 ℓ
Answer(s): 20 ℓ