The figure shows 2 tanks, Tank U and Tank V. Tank V is completely empty while Tank U is filled with water to the brim. Water from Tap T flows in at a rate of 3.6 litres per minute while water drains from Tap S at a rate of 0.72 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 U
= 50 x 20
= 1000 cm
2 1 ℓ = 1000 cm
3 3.6 ℓ = 3600 cm
3 0.72 ℓ = 720 cm
3 Height increase per minute for Tank U
= 3600 ÷ 1000
= 3.6 cm/min
Base area of Tank V
= 30 x 20
= 600 cm
2 Height decrease per minute for Tank V
= 720 ÷ 600
= 1.2 cm/min
Let t be the time taken for both the water levels to become the same.
3.6 t = 12 - 1.2 t
4.8 t = 12
1 t = 2.5 min
(b)
Height of the water level
= 3.6 t
= 3.6 x 2.5
= 9 cm
Answer(s): (a) 2.5 min; (b) 9 cm