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 7.2 litres per minute while water drains from Tap N 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 Q
= 30 x 15
= 450 cm
2 1 ℓ = 1000 cm
3 7.2 ℓ = 7200 cm
3 1.44 ℓ = 1440 cm
3 Height increase per minute for Container Q
= 7200 ÷ 450
= 16 cm/min
Base area of Container R
= 40 x 24
= 960 cm
2 Height decrease per minute for Container R
= 1440 ÷ 960
= 1.5 cm/min
Let t be the time taken for both the water levels to become the same.
16 t = 14 - 1.5 t
17.5 t = 14
1 t = 0.8 min
(b)
Height of the water level
= 16 t
= 16 x 0.8
= 12.8 cm
Answer(s): (a) 0.8 min; (b) 12.8 cm