The figure shows 2 containers, Container D and Container E. Container E is completely empty while Container D is filled with water to the brim. Water from Tap C flows in at a rate of 2.4 litres per minute while water drains from Tap B at a rate of 1.44 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 D
= 50 x 15
= 750 cm
2 1 ℓ = 1000 cm
3 2.4 ℓ = 2400 cm
3 1.44 ℓ = 1440 cm
3 Height increase per minute for Container D
= 2400 ÷ 750
= 3.2 cm/min
Base area of Container E
= 40 x 20
= 800 cm
2 Height decrease per minute for Container E
= 1440 ÷ 800
= 1.8 cm/min
Let t be the time taken for both the water levels to become the same.
3.2 t = 12 - 1.8 t
5 t = 12
1 t = 2.4 min
(b)
Height of the water level
= 3.2 t
= 3.2 x 2.4
= 7.68 cm
Answer(s): (a) 2.4 min; (b) 7.68 cm