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 1.44 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
= 40 x 25
= 1000 cm
2 1 ℓ = 1000 cm
3 1.2 ℓ = 1200 cm
3 1.44 ℓ = 1440 cm
3 Height increase per minute for Container Y
= 1200 ÷ 1000
= 1.2 cm/min
Base area of Container Z
= 40 x 20
= 800 cm
2 Height decrease per minute for Container Z
= 1440 ÷ 800
= 1.8 cm/min
Let t be the time taken for both the water levels to become the same.
1.2 t = 12 - 1.8 t
3 t = 12
1 t = 4 min
(b)
Height of the water level
= 1.2 t
= 1.2 x 4
= 4.8 cm
Answer(s): (a) 4 min; (b) 4.8 cm