William has 2 containers. Container V and Container W are of different capacities. If Container V is filled by a tap at a rate of 5 litres per minute and Container W is filled by a tap at a rate of 7 litres per minute, when Container V is completely filled, 7 litres of water flowed out from Container W. If Container V is filled by a tap at a rate of 6 litres per minute and Container W is filled by a tap at a rate of 4 litres per minute, when Container V is completely filled, Container W is only half-filled. What is the capacity of Container W? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container V |
Container W |
Container V |
Container W |
Volume of the container |
5 u |
7 u - 7 |
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.
5 u = 6 p --- (1)
7 u - 7 = 8 p
7 u = 8 p + 7 --- (2)
Make u the same.
(1) x 7
35 u = 42 p --- (3)
(2) x 5
35 u = 40 p + 35 --- (4)
(3) = (4)
42 p = 40 p + 35
42 p - 40 p = 35
2 p = 35
1 p = 35 ÷ 2 = 17.5
Volume of Container W
= 8 p
= 8 x 17.5
= 140 ℓ
Answer(s): 140 ℓ