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 7.2 litres per minute while water drains from Tap P at a rate of 2.16 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 15
= 450 cm
2 1 ℓ = 1000 cm
3 7.2 ℓ = 7200 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Container R
= 7200 ÷ 450
= 16 cm/min
Base area of Container S
= 30 x 18
= 540 cm
2 Height decrease per minute for Container S
= 2160 ÷ 540
= 4 cm/min
Let t be the time taken for both the water levels to become the same.
16 t = 14 - 4 t
20 t = 14
1 t = 0.7 min
(b)
Height of the water level
= 16 t
= 16 x 0.7
= 11.2 cm
Answer(s): (a) 0.7 min; (b) 11.2 cm