Sophia has 2 tanks. Tank W and Tank X are of different capacities. If Tank W is filled by a tap at a rate of 4 litres per minute and Tank X is filled by a tap at a rate of 6 litres per minute, when Tank W is completely filled, 7 litres of water flowed out from Tank X. If Tank W is filled by a tap at a rate of 4 litres per minute and Tank X is filled by a tap at a rate of 2 litres per minute, when Tank W is completely filled, Tank X is only half-filled. What is the capacity of Tank X? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank W |
Tank X |
Tank W |
Tank X |
Volume of the tank |
4 u |
6 u - 7 |
4 p |
2 p x 2 = 4 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)
6 u - 7 = 4 p
6 u = 4 p + 7 --- (2)
Make u the same.
(1) x 3
12 u = 12 p --- (3)
(2) x 2
12 u = 8 p + 14 --- (4)
(3) = (4)
12 p = 8 p + 14
12 p - 8 p = 14
4 p = 14
1 p = 14 ÷ 4 = 3.5
Volume of Tank X
= 4 p
= 4 x 3.5
= 14 ℓ
Answer(s): 14 ℓ