The figure shows 2 containers, Container G and Container H. Container H is completely empty while Container G is filled with water to the brim. Water from Tap F flows in at a rate of 3.6 litres per minute while water drains from Tap E 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 G
= 30 x 15
= 450 cm
2 1 ℓ = 1000 cm
3 3.6 ℓ = 3600 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Container G
= 3600 ÷ 450
= 8 cm/min
Base area of Container H
= 20 x 24
= 480 cm
2 Height decrease per minute for Container H
= 2160 ÷ 480
= 4.5 cm/min
Let t be the time taken for both the water levels to become the same.
8 t = 10 - 4.5 t
12.5 t = 10
1 t = 0.8 min
(b)
Height of the water level
= 8 t
= 8 x 0.8
= 6.4 cm
Answer(s): (a) 0.8 min; (b) 6.4 cm