Christopher has 2 tanks. Tank R and Tank S are of different capacities. If Tank R is filled by a tap at a rate of 3 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, 5 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 4 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 |
3 u |
7 u - 5 |
4 p |
4 p x 2 = 8 p |
Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.
3 u = 4 p --- (1)
7 u - 5 = 8 p
7 u = 8 p + 5 --- (2)
Make u the same.
(1) x 7
21 u = 28 p --- (3)
(2) x 3
21 u = 24 p + 15 --- (4)
(3) = (4)
28 p = 24 p + 15
28 p - 24 p = 15
4 p = 15
1 p = 15 ÷ 4 = 3.75
Volume of Tank S
= 8 p
= 8 x 3.75
= 30 ℓ
Answer(s): 30 ℓ