The figure shows 2 containers, Container S and Container T. Container T is completely empty while Container S is filled with water to the brim. Water from Tap R flows in at a rate of 1.2 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 Container S
= 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 Container S
= 1200 ÷ 600
= 2 cm/min
Base area of Container T
= 20 x 24
= 480 cm
2 Height decrease per minute for Container T
= 1440 ÷ 480
= 3 cm/min
Let t be the time taken for both the water levels to become the same.
2 t = 14 - 3 t
5 t = 14
1 t = 2.8 min
(b)
Height of the water level
= 2 t
= 2 x 2.8
= 5.6 cm
Answer(s): (a) 2.8 min; (b) 5.6 cm