The figure shows 2 containers, Container Y and Container Z. Container Z is completely empty while Container Y is filled with water to the brim. Water from Tap X flows in at a rate of 1.2 litres per minute while water drains from Tap W 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 Y
= 30 x 20
= 600 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 Y
= 1200 ÷ 600
= 2 cm/min
Base area of Container Z
= 20 x 18
= 360 cm
2 Height decrease per minute for Container Z
= 720 ÷ 360
= 2 cm/min
Let t be the time taken for both the water levels to become the same.
2 t = 14 - 2 t
4 t = 14
1 t = 3.5 min
(b)
Height of the water level
= 2 t
= 2 x 3.5
= 7 cm
Answer(s): (a) 3.5 min; (b) 7 cm