Jackson has 2 tanks. Tank V and Tank W are of different capacities. If Tank V is filled by a tap at a rate of 4 litres per minute and Tank W is filled by a tap at a rate of 5 litres per minute, when Tank V is completely filled, 7 litres of water flowed out from Tank W. If Tank V is filled by a tap at a rate of 6 litres per minute and Tank W is filled by a tap at a rate of 2 litres per minute, when Tank V is completely filled, Tank W is only half-filled. What is the capacity of Tank W? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank V |
Tank W |
Tank V |
Tank W |
Volume of the tank |
4 u |
5 u - 7 |
6 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 = 6 p --- (1)
5 u - 7 = 4 p
5 u = 4 p + 7 --- (2)
Make u the same.
(1) x 5
20 u = 30 p --- (3)
(2) x 4
20 u = 16 p + 28 --- (4)
(3) = (4)
30 p = 16 p + 28
30 p - 16 p = 28
14 p = 28
1 p = 28 ÷ 14 = 2
Volume of Tank W
= 4 p
= 4 x 2
= 8 ℓ
Answer(s): 8 ℓ