Harper has 2 containers. Container B and Container C are of different capacities. If Container B is filled by a tap at a rate of 5 litres per minute and Container C is filled by a tap at a rate of 7 litres per minute, when Container B is completely filled, 5 litres of water flowed out from Container C. If Container B is filled by a tap at a rate of 6 litres per minute and Container C is filled by a tap at a rate of 2 litres per minute, when Container B is completely filled, Container C is only one-quarter-filled. What is the capacity of Container C? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container B |
Container C |
Container B |
Container C |
Volume of the container |
5 u |
7 u - 5 |
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.
5 u = 6 p --- (1)
7 u - 5 = 8 p
7 u = 8 p + 5 --- (2)
Make u the same.
(1) x 7
35 u = 42 p --- (3)
(2) x 5
35 u = 40 p + 25 --- (4)
(3) = (4)
42 p = 40 p + 25
42 p - 40 p = 25
2 p = 25
1 p = 25 ÷ 2 = 12.5
Volume of Container C
= 8 p
= 8 x 12.5
= 100 ℓ
Answer(s): 100 ℓ