Benjamin has 2 tanks. Tank Q and Tank R are of different capacities. If Tank Q is filled by a tap at a rate of 3 litres per minute and Tank R is filled by a tap at a rate of 7 litres per minute, when Tank Q is completely filled, 6 litres of water flowed out from Tank R. If Tank Q is filled by a tap at a rate of 6 litres per minute and Tank R is filled by a tap at a rate of 2 litres per minute, when Tank Q is completely filled, Tank R is only one-quarter-filled. What is the capacity of Tank R? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank Q |
Tank R |
Tank Q |
Tank R |
Volume of the tank |
3 u |
7 u - 6 |
6 p |
2 p x 4 = 8 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 = 8 p
7 u = 8 p + 6 --- (2)
Make u the same.
(1) x 7
21 u = 42 p --- (3)
(2) x 3
21 u = 24 p + 18 --- (4)
(3) = (4)
42 p = 24 p + 18
42 p - 24 p = 18
18 p = 18
1 p = 18 ÷ 18 = 1
Volume of Tank R
= 8 p
= 8 x 1
= 8 ℓ
Answer(s): 8 ℓ