Andrew has 2 tanks. Tank T and Tank U are of different capacities. If Tank T is filled by a tap at a rate of 3 litres per minute and Tank U is filled by a tap at a rate of 7 litres per minute, when Tank T is completely filled, 5 litres of water flowed out from Tank U. If Tank T is filled by a tap at a rate of 3 litres per minute and Tank U is filled by a tap at a rate of 2 litres per minute, when Tank T is completely filled, Tank U is only one-third-filled. What is the capacity of Tank U? Express your answer in litres.
|
Scenario 1 |
Scenario 2 |
Tank type |
Tank T |
Tank U |
Tank T |
Tank U |
Volume of the tank |
3 u |
7 u - 5 |
3 p |
2 p x 3 = 6 p |
Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.
3 u = 3 p --- (1)
7 u - 5 = 6 p
7 u = 6 p + 5 --- (2)
Make u the same.
(1) x 7
21 u = 21 p --- (3)
(2) x 3
21 u = 18 p + 15 --- (4)
(3) = (4)
21 p = 18 p + 15
21 p - 18 p = 15
3 p = 15
1 p = 15 ÷ 3 = 5
Volume of Tank U
= 6 p
= 6 x 5
= 30 ℓ
Answer(s): 30 ℓ