The figure shows 2 tanks, Tank V and Tank W. Tank W is completely empty while Tank V is filled with water to the brim. Water from Tap U flows in at a rate of 7.2 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 Tank V
= 30 x 20
= 600 cm
2 1 ℓ = 1000 cm
3 7.2 ℓ = 7200 cm
3 1.44 ℓ = 1440 cm
3 Height increase per minute for Tank V
= 7200 ÷ 600
= 12 cm/min
Base area of Tank W
= 40 x 18
= 720 cm
2 Height decrease per minute for Tank W
= 1440 ÷ 720
= 2 cm/min
Let t be the time taken for both the water levels to become the same.
12 t = 14 - 2 t
14 t = 14
1 t = 1 min
(b)
Height of the water level
= 12 t
= 12 x 1
= 12 cm
Answer(s): (a) 1 min; (b) 12 cm