Michael 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 5 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 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 half-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 |
5 u - 6 |
3 p |
2 p x 2 = 4 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)
5 u - 6 = 4 p
5 u = 4 p + 6 --- (2)
Make u the same.
(1) x 5
15 u = 15 p --- (3)
(2) x 3
15 u = 12 p + 18 --- (4)
(3) = (4)
15 p = 12 p + 18
15 p - 12 p = 18
3 p = 18
1 p = 18 ÷ 3 = 6
Volume of Tank U
= 4 p
= 4 x 6
= 24 ℓ
Answer(s): 24 ℓ