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 4.8 litres per minute while water drains from Tap D at a rate of 0.72 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 4.8 ℓ = 4800 cm
3 0.72 ℓ = 720 cm
3 Height increase per minute for Container F
= 4800 ÷ 600
= 8 cm/min
Base area of Container G
= 40 x 24
= 960 cm
2 Height decrease per minute for Container G
= 720 ÷ 960
= 0.75 cm/min
Let t be the time taken for both the water levels to become the same.
8 t = 14 - 0.75 t
8.75 t = 14
1 t = 1.6 min
(b)
Height of the water level
= 8 t
= 8 x 1.6
= 12.8 cm
Answer(s): (a) 1.6 min; (b) 12.8 cm