The figure shows 2 tanks, Tank P and Tank Q. Tank Q is completely empty while Tank P is filled with water to the brim. Water from Tap N flows in at a rate of 3.6 litres per minute while water drains from Tap M 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 P
= 40 x 15
= 600 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 P
= 3600 ÷ 600
= 6 cm/min
Base area of Tank Q
= 30 x 24
= 720 cm
2 Height decrease per minute for Tank Q
= 1440 ÷ 720
= 2 cm/min
Let t be the time taken for both the water levels to become the same.
6 t = 16 - 2 t
8 t = 16
1 t = 2 min
(b)
Height of the water level
= 6 t
= 6 x 2
= 12 cm
Answer(s): (a) 2 min; (b) 12 cm