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 2.7 litres per minute. After 6 minutes, tap B was turned on. At 11.10 p.m., the tank was half filled with water.
- How many litres of water flowed out of tap B in 1 minute?
- At 11.20 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 11.10 p.m. when it was half filled with water
= 27 ÷ 2
= 13.5 ℓ
Volume of water by Tap A for 6 min
= 6 x 2.7
= 16.2 ℓ
Duration that Tap B was turned
= 10 - 6
= 4 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 4 min
= 16.2 - 13.5
= 2.7 ℓ
Volume of water that flowed out in 1 min
= 2.7 ÷ 4
= 0.675 ℓ
Volume of water that flowed out of Tap B in 1 min
= 2.7 + 0.675
= 3.375 ℓ
(b)
Duration from 11.10 p.m. to 11.20 p.m. = 10 min
Volume of water that flowed out from 11.10 p.m. to 11.20 p.m.
= 10 x 0.675
= 6.75 ℓ
Volume of water left at 11.20 p.m.
= 13.5 - 6.75
= 6.75 ℓ
Fraction of the tank filled with water at 11.20 p.m.
=
6.7527 =
14
Answer(s): (a) 3.375 ℓ; (b) 14