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 1.2 litres per minute while water drains from Tap S 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 U
= 40 x 15
= 600 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 U
= 1200 ÷ 600
= 2 cm/min
Base area of Tank V
= 20 x 24
= 480 cm
2 Height decrease per minute for Tank V
= 1440 ÷ 480
= 3 cm/min
Let t be the time taken for both the water levels to become the same.
2 t = 12 - 3 t
5 t = 12
1 t = 2.4 min
(b)
Height of the water level
= 2 t
= 2 x 2.4
= 4.8 cm
Answer(s): (a) 2.4 min; (b) 4.8 cm