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 4.2 litres per minute. After 7 minutes, tap B was turned on. At 11.12 p.m., the tank was half filled with water.
- How many litres of water flowed out of tap B in 1 minute?
- At 11.27 p.m., what fraction of the tank was filled with water?
(a)
Volume of the tank
= 60 x 35 x 25
= 52500 mℓ
= 52.5 ℓ
Volume of the tank at 11.12 p.m. when it was half filled with water
= 52.5 ÷ 2
= 26.25 ℓ
Volume of water by Tap A for 7 min
= 7 x 4.2
= 29.4 ℓ
Duration that Tap B was turned
= 12 - 7
= 5 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 5 min
= 29.4 - 26.25
= 3.15 ℓ
Volume of water that flowed out in 1 min
= 3.15 ÷ 5
= 0.63 ℓ
Volume of water that flowed out of Tap B in 1 min
= 4.2 + 0.63
= 4.83 ℓ
(b)
Duration from 11.12 p.m. to 11.27 p.m. = 15 min
Volume of water that flowed out from 11.12 p.m. to 11.27 p.m.
= 15 x 0.63
= 9.45 ℓ
Volume of water left at 11.27 p.m.
= 26.25 - 9.45
= 16.8 ℓ
Fraction of the tank filled with water at 11.27 p.m.
=
16.852.5 =
825
Answer(s): (a) 4.83 ℓ; (b) 825