The figure shows 2 tanks, Tank H and Tank J. Tank J is completely empty while Tank H is filled with water to the brim. Water from Tap G flows in at a rate of 3.6 litres per minute while water drains from Tap F 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 Tank H
= 30 x 20
= 600 cm
2 1 ℓ = 1000 cm
3 3.6 ℓ = 3600 cm
3 0.72 ℓ = 720 cm
3 Height increase per minute for Tank H
= 3600 ÷ 600
= 6 cm/min
Base area of Tank J
= 20 x 18
= 360 cm
2 Height decrease per minute for Tank J
= 720 ÷ 360
= 2 cm/min
Let t be the time taken for both the water levels to become the same.
6 t = 12 - 2 t
8 t = 12
1 t = 1.5 min
(b)
Height of the water level
= 6 t
= 6 x 1.5
= 9 cm
Answer(s): (a) 1.5 min; (b) 9 cm