The figure shows 2 containers, Container V and Container W. Container W is completely empty while Container V is filled with water to the brim. Water from Tap U flows in at a rate of 2.4 litres per minute while water drains from Tap T at a rate of 2.16 litres per minute. Both taps are turned on at the same time. After some time, the heights of the water level in both tanks became the same.
- Find the time taken for the heights of the water level to be the same in both tanks.
- Find the height of the water level at that point of time.
(a)
Base area of Container V
= 50 x 20
= 1000 cm
2 1 ℓ = 1000 cm
3 2.4 ℓ = 2400 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Container V
= 2400 ÷ 1000
= 2.4 cm/min
Base area of Container W
= 30 x 18
= 540 cm
2 Height decrease per minute for Container W
= 2160 ÷ 540
= 4 cm/min
Let t be the time taken for both the water levels to become the same.
2.4 t = 16 - 4 t
6.4 t = 16
1 t = 2.5 min
(b)
Height of the water level
= 2.4 t
= 2.4 x 2.5
= 6 cm
Answer(s): (a) 2.5 min; (b) 6 cm