Caleb has 2 tanks. Tank Q and Tank R are of different capacities. If Tank Q is filled by a tap at a rate of 4 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, 5 litres of water flowed out from Tank R. If Tank Q is filled by a tap at a rate of 4 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-third-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 |
4 u |
7 u - 5 |
4 p |
2 p x 3 = 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 - 5 = 6 p
7 u = 6 p + 5 --- (2)
Make u the same.
(1) x 7
28 u = 28 p --- (3)
(2) x 4
28 u = 24 p + 20 --- (4)
(3) = (4)
28 p = 24 p + 20
28 p - 24 p = 20
4 p = 20
1 p = 20 ÷ 4 = 5
Volume of Tank R
= 6 p
= 6 x 5
= 30 ℓ
Answer(s): 30 ℓ