Lily has 2 tanks. Tank E and Tank F are of different capacities. If Tank E is filled by a tap at a rate of 3 litres per minute and Tank F is filled by a tap at a rate of 5 litres per minute, when Tank E is completely filled, 7 litres of water flowed out from Tank F. If Tank E is filled by a tap at a rate of 6 litres per minute and Tank F is filled by a tap at a rate of 3 litres per minute, when Tank E is completely filled, Tank F is only one-third-filled. What is the capacity of Tank F? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank E |
Tank F |
Tank E |
Tank F |
Volume of the tank |
3 u |
5 u - 7 |
6 p |
3 p x 3 = 9 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 = 9 p
5 u = 9 p + 7 --- (2)
Make u the same.
(1) x 5
15 u = 30 p --- (3)
(2) x 3
15 u = 27 p + 21 --- (4)
(3) = (4)
30 p = 27 p + 21
30 p - 27 p = 21
3 p = 21
1 p = 21 ÷ 3 = 7
Volume of Tank F
= 9 p
= 9 x 7
= 63 ℓ
Answer(s): 63 ℓ