Leah has 2 tanks. Tank E and Tank F are of different capacities. If Tank E is filled by a tap at a rate of 4 litres per minute and Tank F is filled by a tap at a rate of 7 litres per minute, when Tank E is completely filled, 5 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 4 litres per minute, when Tank E is completely filled, Tank F is only half-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 |
4 u |
7 u - 5 |
6 p |
4 p x 2 = 8 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 = 8 p
7 u = 8 p + 5 --- (2)
Make u the same.
(1) x 7
28 u = 42 p --- (3)
(2) x 4
28 u = 32 p + 20 --- (4)
(3) = (4)
42 p = 32 p + 20
42 p - 32 p = 20
10 p = 20
1 p = 20 ÷ 10 = 2
Volume of Tank F
= 8 p
= 8 x 2
= 16 ℓ
Answer(s): 16 ℓ