The figure shows 2 tanks, Tank Z and Tank A. Tank A is completely empty while Tank 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 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 Tank Z
= 30 x 20
= 600 cm
2 1 ℓ = 1000 cm
3 1.2 ℓ = 1200 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Tank Z
= 1200 ÷ 600
= 2 cm/min
Base area of Tank A
= 30 x 24
= 720 cm
2 Height decrease per minute for Tank A
= 2160 ÷ 720
= 3 cm/min
Let t be the time taken for both the water levels to become the same.
2 t = 16 - 3 t
5 t = 16
1 t = 3.2 min
(b)
Height of the water level
= 2 t
= 2 x 3.2
= 6.4 cm
Answer(s): (a) 3.2 min; (b) 6.4 cm