The figure shows 2 tanks, Tank X and Tank Y. Tank Y is completely empty while Tank X is filled with water to the brim. Water from Tap W flows in at a rate of 1.2 litres per minute while water drains from Tap V 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 X
= 50 x 20
= 1000 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 X
= 1200 ÷ 1000
= 1.2 cm/min
Base area of Tank Y
= 40 x 18
= 720 cm
2 Height decrease per minute for Tank Y
= 1440 ÷ 720
= 2 cm/min
Let t be the time taken for both the water levels to become the same.
1.2 t = 16 - 2 t
3.2 t = 16
1 t = 5 min
(b)
Height of the water level
= 1.2 t
= 1.2 x 5
= 6 cm
Answer(s): (a) 5 min; (b) 6 cm