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 7.2 litres per minute while water drains from Tap W at a rate of 2.16 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
= 50 x 20
= 1000 cm
2 1 ℓ = 1000 cm
3 7.2 ℓ = 7200 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Container Y
= 7200 ÷ 1000
= 7.2 cm/min
Base area of Container Z
= 30 x 18
= 540 cm
2 Height decrease per minute for Container Z
= 2160 ÷ 540
= 4 cm/min
Let t be the time taken for both the water levels to become the same.
7.2 t = 14 - 4 t
11.2 t = 14
1 t = 1.25 min
(b)
Height of the water level
= 7.2 t
= 7.2 x 1.25
= 9 cm
Answer(s): (a) 1.25 min; (b) 9 cm