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 4.8 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
= 30 x 25
= 750 cm
2 1 ℓ = 1000 cm
3 4.8 ℓ = 4800 cm
3 1.44 ℓ = 1440 cm
3 Height increase per minute for Container V
= 4800 ÷ 750
= 6.4 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.
6.4 t = 16 - 3.6 t
10 t = 16
1 t = 1.6 min
(b)
Height of the water level
= 6.4 t
= 6.4 x 1.6
= 10.24 cm
Answer(s): (a) 1.6 min; (b) 10.24 cm