The figure shows 2 tanks, Tank Q and Tank R. Tank R is completely empty while Tank Q is filled with water to the brim. Water from Tap P flows in at a rate of 2.4 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 Tank Q
= 40 x 15
= 600 cm
2 1 ℓ = 1000 cm
3 2.4 ℓ = 2400 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Tank Q
= 2400 ÷ 600
= 4 cm/min
Base area of Tank R
= 30 x 18
= 540 cm
2 Height decrease per minute for Tank R
= 2160 ÷ 540
= 4 cm/min
Let t be the time taken for both the water levels to become the same.
4 t = 12 - 4 t
8 t = 12
1 t = 1.5 min
(b)
Height of the water level
= 4 t
= 4 x 1.5
= 6 cm
Answer(s): (a) 1.5 min; (b) 6 cm