Evan 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, 6 litres of water flowed out from Tank U. If Tank T is filled by a tap at a rate of 5 litres per minute and Tank U is filled by a tap at a rate of 3 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 - 6 |
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 - 6 = 9 p
7 u = 9 p + 6 --- (2)
Make u the same.
(1) x 7
21 u = 35 p --- (3)
(2) x 3
21 u = 27 p + 18 --- (4)
(3) = (4)
35 p = 27 p + 18
35 p - 27 p = 18
8 p = 18
1 p = 18 ÷ 8 = 2.25
Volume of Tank U
= 9 p
= 9 x 2.25
= 20.25 ℓ
Answer(s): 20.25 ℓ