The figure shows 2 tanks, Tank Q and Tank R. Tank R is completely empty while Tank Q is filled with water to the brim. Water from Tap P flows in at a rate of 1.2 litres per minute while water drains from Tap N 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 Q
= 40 x 20
= 800 cm
2 1 ℓ = 1000 cm
3 1.2 ℓ = 1200 cm
3 1.44 ℓ = 1440 cm
3 Height increase per minute for Tank Q
= 1200 ÷ 800
= 1.5 cm/min
Base area of Tank R
= 40 x 24
= 960 cm
2 Height decrease per minute for Tank R
= 1440 ÷ 960
= 1.5 cm/min
Let t be the time taken for both the water levels to become the same.
1.5 t = 12 - 1.5 t
3 t = 12
1 t = 4 min
(b)
Height of the water level
= 1.5 t
= 1.5 x 4
= 6 cm
Answer(s): (a) 4 min; (b) 6 cm