The figure shows 2 containers, Container E and Container F. Container F is completely empty while Container E is filled with water to the brim. Water from Tap D flows in at a rate of 2.4 litres per minute while water drains from Tap C 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 E
= 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 E
= 2400 ÷ 1000
= 2.4 cm/min
Base area of Container F
= 30 x 20
= 600 cm
2 Height decrease per minute for Container F
= 2160 ÷ 600
= 3.6 cm/min
Let t be the time taken for both the water levels to become the same.
2.4 t = 12 - 3.6 t
6 t = 12
1 t = 2 min
(b)
Height of the water level
= 2.4 t
= 2.4 x 2
= 4.8 cm
Answer(s): (a) 2 min; (b) 4.8 cm