The figure shows 2 tanks, Tank J and Tank K. Tank K is completely empty while Tank J is filled with water to the brim. Water from Tap H flows in at a rate of 3.6 litres per minute while water drains from Tap G 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 J
= 30 x 20
= 600 cm
2 1 ℓ = 1000 cm
3 3.6 ℓ = 3600 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Tank J
= 3600 ÷ 600
= 6 cm/min
Base area of Tank K
= 30 x 18
= 540 cm
2 Height decrease per minute for Tank K
= 2160 ÷ 540
= 4 cm/min
Let t be the time taken for both the water levels to become the same.
6 t = 12 - 4 t
10 t = 12
1 t = 1.2 min
(b)
Height of the water level
= 6 t
= 6 x 1.2
= 7.2 cm
Answer(s): (a) 1.2 min; (b) 7.2 cm