Chloe has 2 containers. Container Q and Container R are of different capacities. If Container Q is filled by a tap at a rate of 3 litres per minute and Container R is filled by a tap at a rate of 7 litres per minute, when Container Q is completely filled, 6 litres of water flowed out from Container R. If Container Q is filled by a tap at a rate of 6 litres per minute and Container R is filled by a tap at a rate of 5 litres per minute, when Container Q is completely filled, Container R is only half-filled. What is the capacity of Container R? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container Q |
Container R |
Container Q |
Container R |
Volume of the container |
3 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.
3 u = 6 p --- (1)
7 u - 6 = 10 p
7 u = 10 p + 6 --- (2)
Make u the same.
(1) x 7
21 u = 42 p --- (3)
(2) x 3
21 u = 30 p + 18 --- (4)
(3) = (4)
42 p = 30 p + 18
42 p - 30 p = 18
12 p = 18
1 p = 18 ÷ 12 = 1.5
Volume of Container R
= 10 p
= 10 x 1.5
= 15 ℓ
Answer(s): 15 ℓ