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 7.2 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 25
= 750 cm
2 1 ℓ = 1000 cm
3 7.2 ℓ = 7200 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Tank J
= 7200 ÷ 750
= 9.6 cm/min
Base area of Tank K
= 20 x 20
= 400 cm
2 Height decrease per minute for Tank K
= 2160 ÷ 400
= 5.4 cm/min
Let t be the time taken for both the water levels to become the same.
9.6 t = 12 - 5.4 t
15 t = 12
1 t = 0.8 min
(b)
Height of the water level
= 9.6 t
= 9.6 x 0.8
= 7.68 cm
Answer(s): (a) 0.8 min; (b) 7.68 cm