The figure shows 2 tanks, Tank F and Tank G. Tank G is completely empty while Tank F is filled with water to the brim. Water from Tap E flows in at a rate of 3.6 litres per minute while water drains from Tap D at a rate of 1.44 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 F
= 50 x 20
= 1000 cm
2 1 ℓ = 1000 cm
3 3.6 ℓ = 3600 cm
3 1.44 ℓ = 1440 cm
3 Height increase per minute for Tank F
= 3600 ÷ 1000
= 3.6 cm/min
Base area of Tank G
= 30 x 24
= 720 cm
2 Height decrease per minute for Tank G
= 1440 ÷ 720
= 2 cm/min
Let t be the time taken for both the water levels to become the same.
3.6 t = 14 - 2 t
5.6 t = 14
1 t = 2.5 min
(b)
Height of the water level
= 3.6 t
= 3.6 x 2.5
= 9 cm
Answer(s): (a) 2.5 min; (b) 9 cm