PSLE The figure shows taps A and B and an empty tank. At 3 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 6 minutes, tap B was turned on. At 3.10 p.m., the tank was half filled with water.
- How many litres of water flowed out of tap B in 1 minute?
- At 3.20 p.m., what fraction of the tank was filled with water?
(a)
Volume of the tank
= 60 x 30 x 25
= 45000 mℓ
= 45 ℓ
Volume of the tank at 3.10 p.m. when it was half filled with water
= 45 ÷ 2
= 22.5 ℓ
Volume of water by Tap A for 6 min
= 6 x 4.2
= 25.2 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
= 25.2 - 22.5
= 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
= 4.2 + 0.675
= 4.875 ℓ
(b)
Duration from 3.10 p.m. to 3.20 p.m. = 10 min
Volume of water that flowed out from 3.10 p.m. to 3.20 p.m.
= 10 x 0.675
= 6.75 ℓ
Volume of water left at 3.20 p.m.
= 22.5 - 6.75
= 15.75 ℓ
Fraction of the tank filled with water at 3.20 p.m.
=
15.7545 =
720
Answer(s): (a) 4.875 ℓ; (b) 720