Tao Nan School P6 Math CA1 2004 (Q49)

The tank below was 30% filled with water. Taps A and B were turned on at the same time. Water flowed from Tap A at the rate of 196 cubic cm per second, while Tap B at 100 cubic cm per second.

a) Find the volume of water in the tank before the taps were turned on.
b) How much time was needed to fill 40% of the tank?



Solution

Q(a)

Water was filled up to 30% of the tank. Therefore volume of water in the tank is

80 cm x 40 cm x 30 cm x 30%
= 28 800 cubic cm
= 28.8 litres

Answer: The volume of water in the tank before both taps were turned on was 28.8 litres.


Q(b)

For the tank to be filled up to 40%, water is needed to fill it up by another 10% of the tank.

30% of the volume of the tank holds 28.8 litres.
10% will hold ----- 28.8 litres divided by 3 = 9.6 litres

Tap A had a rate of 196 ml per second, while Tap B 100 ml per second.

Net flow of water into the tank is therefore 196 ml per sec – 100 ml per sec = 96 ml per sec.

Time taken to fill up 9.6 litres -----
9.6 litres divided by 96 ml per sec
= 100 seconds
= 1 min 40 seconds.

Answer: It takes 1 min 40 seconds to fill up to 40% of the tank.