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 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
= 50 x 15
= 750 cm
2 1 ℓ = 1000 cm
3 4.8 ℓ = 4800 cm
3 1.44 ℓ = 1440 cm
3 Height increase per minute for Container Q
= 4800 ÷ 750
= 6.4 cm/min
Base area of Container R
= 20 x 20
= 400 cm
2 Height decrease per minute for Container R
= 1440 ÷ 400
= 3.6 cm/min
Let t be the time taken for both the water levels to become the same.
6.4 t = 14 - 3.6 t
10 t = 14
1 t = 1.4 min
(b)
Height of the water level
= 6.4 t
= 6.4 x 1.4
= 8.96 cm
Answer(s): (a) 1.4 min; (b) 8.96 cm