Jacob 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, 8 litres of water flowed out from Tank U. If Tank T is filled by a tap at a rate of 4 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-quarter-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 - 8 |
4 p |
2 p x 4 = 8 p |
Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.
3 u = 4 p --- (1)
7 u - 8 = 8 p
7 u = 8 p + 8 --- (2)
Make u the same.
(1) x 7
21 u = 28 p --- (3)
(2) x 3
21 u = 24 p + 24 --- (4)
(3) = (4)
28 p = 24 p + 24
28 p - 24 p = 24
4 p = 24
1 p = 24 ÷ 4 = 6
Volume of Tank U
= 8 p
= 8 x 6
= 48 ℓ
Answer(s): 48 ℓ