The figure shows 2 containers, Container Q and Container R. Container R is completely empty while Container Q is filled with water to the brim. Water from Tap P flows in at a rate of 4.8 litres per minute while water drains from Tap N 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 Q
= 40 x 15
= 600 cm
2 1 ℓ = 1000 cm
3 4.8 ℓ = 4800 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Container Q
= 4800 ÷ 600
= 8 cm/min
Base area of Container R
= 20 x 24
= 480 cm
2 Height decrease per minute for Container R
= 2160 ÷ 480
= 4.5 cm/min
Let t be the time taken for both the water levels to become the same.
8 t = 10 - 4.5 t
12.5 t = 10
1 t = 0.8 min
(b)
Height of the water level
= 8 t
= 8 x 0.8
= 6.4 cm
Answer(s): (a) 0.8 min; (b) 6.4 cm