The figure shows 2 containers, Container Z and Container A. Container A is completely empty while Container Z is filled with water to the brim. Water from Tap Y flows in at a rate of 4.8 litres per minute while water drains from Tap X 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 Z
= 40 x 25
= 1000 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 Z
= 4800 ÷ 1000
= 4.8 cm/min
Base area of Container A
= 30 x 20
= 600 cm
2 Height decrease per minute for Container A
= 720 ÷ 600
= 1.2 cm/min
Let t be the time taken for both the water levels to become the same.
4.8 t = 12 - 1.2 t
6 t = 12
1 t = 2 min
(b)
Height of the water level
= 4.8 t
= 4.8 x 2
= 9.6 cm
Answer(s): (a) 2 min; (b) 9.6 cm