The figure shows 2 containers, Container V and Container W. Container W is completely empty while Container V is filled with water to the brim. Water from Tap U flows in at a rate of 3.6 litres per minute while water drains from Tap T 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 Container V
= 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 Container V
= 3600 ÷ 600
= 6 cm/min
Base area of Container W
= 20 x 20
= 400 cm
2 Height decrease per minute for Container W
= 1440 ÷ 400
= 3.6 cm/min
Let t be the time taken for both the water levels to become the same.
6 t = 12 - 3.6 t
9.6 t = 12
1 t = 1.25 min
(b)
Height of the water level
= 6 t
= 6 x 1.25
= 7.5 cm
Answer(s): (a) 1.25 min; (b) 7.5 cm