The figure shows 2 containers, Container P and Container Q. Container Q is completely empty while Container P is filled with water to the brim. Water from Tap N flows in at a rate of 7.2 litres per minute while water drains from Tap M 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 Container P
= 40 x 15
= 600 cm
2 1 ℓ = 1000 cm
3 7.2 ℓ = 7200 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Container P
= 7200 ÷ 600
= 12 cm/min
Base area of Container Q
= 30 x 24
= 720 cm
2 Height decrease per minute for Container Q
= 2160 ÷ 720
= 3 cm/min
Let t be the time taken for both the water levels to become the same.
12 t = 12 - 3 t
15 t = 12
1 t = 0.8 min
(b)
Height of the water level
= 12 t
= 12 x 0.8
= 9.6 cm
Answer(s): (a) 0.8 min; (b) 9.6 cm