PSLE The figure shows taps A and B and an empty tank. At 11 p.m., tap A was turned on. Water flowed into the tank from tap A at a rate of 3.6 litres per minute. After 5 minutes, tap B was turned on. At 11.15 p.m., the tank was half filled with water.
- How many litres of water flowed out of tap B in 1 minute?
- At 11.24 p.m., what fraction of the tank was filled with water?
(a)
Volume of the tank
= 60 x 30 x 15
= 27000 mℓ
= 27 ℓ
Volume of the tank at 11.15 p.m. when it was half filled with water
= 27 ÷ 2
= 13.5 ℓ
Volume of water by Tap A for 5 min
= 5 x 3.6
= 18 ℓ
Duration that Tap B was turned
= 15 - 5
= 10 min
Since there was a decrease in the volume of water in the tank, water flowed out of Tap B at a faster rate than that of Tap A.
Volume of water that flowed out in 10 min
= 18 - 13.5
= 4.5 ℓ
Volume of water that flowed out in 1 min
= 4.5 ÷ 10
= 0.45 ℓ
Volume of water that flowed out of Tap B in 1 min
= 3.6 + 0.45
= 4.05 ℓ
(b)
Duration from 11.15 p.m. to 11.24 p.m. = 9 min
Volume of water that flowed out from 11.15 p.m. to 11.24 p.m.
= 9 x 0.45
= 4.05 ℓ
Volume of water left at 11.24 p.m.
= 13.5 - 4.05
= 9.45 ℓ
Fraction of the tank filled with water at 11.24 p.m.
=
9.4527 =
720
Answer(s): (a) 4.05 ℓ; (b) 720