Benjamin has 2 tanks. Tank X and Tank Y are of different capacities. If Tank X is filled by a tap at a rate of 3 litres per minute and Tank Y is filled by a tap at a rate of 7 litres per minute, when Tank X is completely filled, 8 litres of water flowed out from Tank Y. If Tank X is filled by a tap at a rate of 5 litres per minute and Tank Y is filled by a tap at a rate of 3 litres per minute, when Tank X is completely filled, Tank Y is only one-third-filled. What is the capacity of Tank Y? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank X |
Tank Y |
Tank X |
Tank Y |
Volume of the tank |
3 u |
7 u - 8 |
5 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 = 5 p --- (1)
7 u - 8 = 9 p
7 u = 9 p + 8 --- (2)
Make u the same.
(1) x 7
21 u = 35 p --- (3)
(2) x 3
21 u = 27 p + 24 --- (4)
(3) = (4)
35 p = 27 p + 24
35 p - 27 p = 24
8 p = 24
1 p = 24 ÷ 8 = 3
Volume of Tank Y
= 9 p
= 9 x 3
= 27 ℓ
Answer(s): 27 ℓ