Emma has 2 tanks. Tank W and Tank X are of different capacities. If Tank W is filled by a tap at a rate of 5 litres per minute and Tank X is filled by a tap at a rate of 7 litres per minute, when Tank W is completely filled, 6 litres of water flowed out from Tank X. If Tank W is filled by a tap at a rate of 5 litres per minute and Tank X is filled by a tap at a rate of 3 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 |
5 u |
7 u - 6 |
5 p |
3 p x 2 = 6 p |
Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.
5 u = 5 p --- (1)
7 u - 6 = 6 p
7 u = 6 p + 6 --- (2)
Make u the same.
(1) x 7
35 u = 35 p --- (3)
(2) x 5
35 u = 30 p + 30 --- (4)
(3) = (4)
35 p = 30 p + 30
35 p - 30 p = 30
5 p = 30
1 p = 30 ÷ 5 = 6
Volume of Tank X
= 6 p
= 6 x 6
= 36 ℓ
Answer(s): 36 ℓ