The figure shows 2 containers, Container F and Container G. Container G is completely empty while Container F is filled with water to the brim. Water from Tap E flows in at a rate of 2.4 litres per minute while water drains from Tap D 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 F
= 40 x 15
= 600 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 F
= 2400 ÷ 600
= 4 cm/min
Base area of Container G
= 20 x 18
= 360 cm
2 Height decrease per minute for Container G
= 1440 ÷ 360
= 4 cm/min
Let t be the time taken for both the water levels to become the same.
4 t = 10 - 4 t
8 t = 10
1 t = 1.25 min
(b)
Height of the water level
= 4 t
= 4 x 1.25
= 5 cm
Answer(s): (a) 1.25 min; (b) 5 cm