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 1.2 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 20
= 800 cm
2 1 ℓ = 1000 cm
3 1.2 ℓ = 1200 cm
3 0.72 ℓ = 720 cm
3 Height increase per minute for Container Z
= 1200 ÷ 800
= 1.5 cm/min
Base area of Container A
= 40 x 20
= 800 cm
2 Height decrease per minute for Container A
= 720 ÷ 800
= 0.9 cm/min
Let t be the time taken for both the water levels to become the same.
1.5 t = 12 - 0.9 t
2.4 t = 12
1 t = 5 min
(b)
Height of the water level
= 1.5 t
= 1.5 x 5
= 7.5 cm
Answer(s): (a) 5 min; (b) 7.5 cm