Mia has 2 tanks. Tank A and Tank B are of different capacities. If Tank A is filled by a tap at a rate of 3 litres per minute and Tank B is filled by a tap at a rate of 5 litres per minute, when Tank A is completely filled, 7 litres of water flowed out from Tank B. If Tank A is filled by a tap at a rate of 6 litres per minute and Tank B is filled by a tap at a rate of 2 litres per minute, when Tank A is completely filled, Tank B is only one-quarter-filled. What is the capacity of Tank B? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank A |
Tank B |
Tank A |
Tank B |
Volume of the tank |
3 u |
5 u - 7 |
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)
5 u - 7 = 8 p
5 u = 8 p + 7 --- (2)
Make u the same.
(1) x 5
15 u = 30 p --- (3)
(2) x 3
15 u = 24 p + 21 --- (4)
(3) = (4)
30 p = 24 p + 21
30 p - 24 p = 21
6 p = 21
1 p = 21 ÷ 6 = 3.5
Volume of Tank B
= 8 p
= 8 x 3.5
= 28 ℓ
Answer(s): 28 ℓ