Zoey has 2 containers. Container P and Container Q are of different capacities. If Container P is filled by a tap at a rate of 4 litres per minute and Container Q is filled by a tap at a rate of 7 litres per minute, when Container P is completely filled, 6 litres of water flowed out from Container Q. If Container P is filled by a tap at a rate of 6 litres per minute and Container Q is filled by a tap at a rate of 5 litres per minute, when Container P is completely filled, Container Q is only half-filled. What is the capacity of Container Q? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container P |
Container Q |
Container P |
Container Q |
Volume of the container |
4 u |
7 u - 6 |
6 p |
5 p x 2 = 10 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 = 10 p
7 u = 10 p + 6 --- (2)
Make u the same.
(1) x 7
28 u = 42 p --- (3)
(2) x 4
28 u = 40 p + 24 --- (4)
(3) = (4)
42 p = 40 p + 24
42 p - 40 p = 24
2 p = 24
1 p = 24 ÷ 2 = 12
Volume of Container Q
= 10 p
= 10 x 12
= 120 ℓ
Answer(s): 120 ℓ