The figure shows 2 tanks, Tank S and Tank T. Tank T is completely empty while Tank S is filled with water to the brim. Water from Tap R flows in at a rate of 4.8 litres per minute while water drains from Tap Q 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 S
= 40 x 20
= 800 cm
2 1 ℓ = 1000 cm
3 4.8 ℓ = 4800 cm
3 1.44 ℓ = 1440 cm
3 Height increase per minute for Tank S
= 4800 ÷ 800
= 6 cm/min
Base area of Tank T
= 40 x 18
= 720 cm
2 Height decrease per minute for Tank T
= 1440 ÷ 720
= 2 cm/min
Let t be the time taken for both the water levels to become the same.
6 t = 14 - 2 t
8 t = 14
1 t = 1.75 min
(b)
Height of the water level
= 6 t
= 6 x 1.75
= 10.5 cm
Answer(s): (a) 1.75 min; (b) 10.5 cm