Mason has 2 tanks. Tank R and Tank S are of different capacities. If Tank R is filled by a tap at a rate of 4 litres per minute and Tank S is filled by a tap at a rate of 7 litres per minute, when Tank R is completely filled, 8 litres of water flowed out from Tank S. If Tank R is filled by a tap at a rate of 4 litres per minute and Tank S is filled by a tap at a rate of 3 litres per minute, when Tank R is completely filled, Tank S is only half-filled. What is the capacity of Tank S? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank R |
Tank S |
Tank R |
Tank S |
Volume of the tank |
4 u |
7 u - 8 |
4 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.
4 u = 4 p --- (1)
7 u - 8 = 6 p
7 u = 6 p + 8 --- (2)
Make u the same.
(1) x 7
28 u = 28 p --- (3)
(2) x 4
28 u = 24 p + 32 --- (4)
(3) = (4)
28 p = 24 p + 32
28 p - 24 p = 32
4 p = 32
1 p = 32 ÷ 4 = 8
Volume of Tank S
= 6 p
= 6 x 8
= 48 ℓ
Answer(s): 48 ℓ