Bryan 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, 5 litres of water flowed out from Tank S. If Tank R is filled by a tap at a rate of 6 litres per minute and Tank S is filled by a tap at a rate of 5 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 - 5 |
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.
4 u = 6 p --- (1)
7 u - 5 = 10 p
7 u = 10 p + 5 --- (2)
Make u the same.
(1) x 7
28 u = 42 p --- (3)
(2) x 4
28 u = 40 p + 20 --- (4)
(3) = (4)
42 p = 40 p + 20
42 p - 40 p = 20
2 p = 20
1 p = 20 ÷ 2 = 10
Volume of Tank S
= 10 p
= 10 x 10
= 100 ℓ
Answer(s): 100 ℓ