PSLE The figure shows taps A and B and an empty tank. At 8 p.m., tap A was turned on. Water flowed into the tank from tap A at a rate of 4.5 litres per minute. After 5 minutes, tap B was turned on. At 8.15 p.m., the tank was half filled with water.
- How many litres of water flowed out of tap B in 1 minute?
- At 8.28 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 8.15 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 4.5
= 22.5 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
= 22.5 - 13.5
= 9 ℓ
Volume of water that flowed out in 1 min
= 9 ÷ 10
= 0.9 ℓ
Volume of water that flowed out of Tap B in 1 min
= 4.5 + 0.9
= 5.4 ℓ
(b)
Duration from 8.15 p.m. to 8.28 p.m. = 13 min
Volume of water that flowed out from 8.15 p.m. to 8.28 p.m.
= 13 x 0.9
= 11.7 ℓ
Volume of water left at 8.28 p.m.
= 13.5 - 11.7
= 1.8 ℓ
Fraction of the tank filled with water at 8.28 p.m.
=
1.827 =
115
Answer(s): (a) 5.4 ℓ; (b) 115