The figure shows 2 tanks, Tank N and Tank P. Tank P is completely empty while Tank N is filled with water to the brim. Water from Tap M flows in at a rate of 2.4 litres per minute while water drains from Tap L 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 N
= 40 x 25
= 1000 cm
2 1 ℓ = 1000 cm
3 2.4 ℓ = 2400 cm
3 1.44 ℓ = 1440 cm
3 Height increase per minute for Tank N
= 2400 ÷ 1000
= 2.4 cm/min
Base area of Tank P
= 30 x 20
= 600 cm
2 Height decrease per minute for Tank P
= 1440 ÷ 600
= 2.4 cm/min
Let t be the time taken for both the water levels to become the same.
2.4 t = 12 - 2.4 t
4.8 t = 12
1 t = 2.5 min
(b)
Height of the water level
= 2.4 t
= 2.4 x 2.5
= 6 cm
Answer(s): (a) 2.5 min; (b) 6 cm