Harper has 2 containers. Container S and Container T are of different capacities. If Container S is filled by a tap at a rate of 3 litres per minute and Container T is filled by a tap at a rate of 5 litres per minute, when Container S is completely filled, 7 litres of water flowed out from Container T. If Container S is filled by a tap at a rate of 6 litres per minute and Container T is filled by a tap at a rate of 3 litres per minute, when Container S is completely filled, Container T is only half-filled. What is the capacity of Container T? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Container type |
Container S |
Container T |
Container S |
Container T |
Volume of the container |
3 u |
5 u - 7 |
6 p |
3 p x 2 = 6 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)
5 u - 7 = 6 p
5 u = 6 p + 7 --- (2)
Make u the same.
(1) x 5
15 u = 30 p --- (3)
(2) x 3
15 u = 18 p + 21 --- (4)
(3) = (4)
30 p = 18 p + 21
30 p - 18 p = 21
12 p = 21
1 p = 21 ÷ 12 = 1.75
Volume of Container T
= 6 p
= 6 x 1.75
= 10.5 ℓ
Answer(s): 10.5 ℓ