The figure shows 2 containers, Container R and Container S. Container S is completely empty while Container R is filled with water to the brim. Water from Tap Q flows in at a rate of 3.6 litres per minute while water drains from Tap P 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 Container R
= 30 x 20
= 600 cm
2 1 ℓ = 1000 cm
3 3.6 ℓ = 3600 cm
3 0.72 ℓ = 720 cm
3 Height increase per minute for Container R
= 3600 ÷ 600
= 6 cm/min
Base area of Container S
= 40 x 18
= 720 cm
2 Height decrease per minute for Container S
= 720 ÷ 720
= 1 cm/min
Let t be the time taken for both the water levels to become the same.
6 t = 14 - 1 t
7 t = 14
1 t = 2 min
(b)
Height of the water level
= 6 t
= 6 x 2
= 12 cm
Answer(s): (a) 2 min; (b) 12 cm