The figure shows 2 tanks, Tank T and Tank U. Tank U is completely empty while Tank T is filled with water to the brim. Water from Tap S flows in at a rate of 4.8 litres per minute while water drains from Tap R 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 T
= 40 x 20
= 800 cm
2 1 ℓ = 1000 cm
3 4.8 ℓ = 4800 cm
3 0.72 ℓ = 720 cm
3 Height increase per minute for Tank T
= 4800 ÷ 800
= 6 cm/min
Base area of Tank U
= 20 x 18
= 360 cm
2 Height decrease per minute for Tank U
= 720 ÷ 360
= 2 cm/min
Let t be the time taken for both the water levels to become the same.
6 t = 10 - 2 t
8 t = 10
1 t = 1.25 min
(b)
Height of the water level
= 6 t
= 6 x 1.25
= 7.5 cm
Answer(s): (a) 1.25 min; (b) 7.5 cm