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 8 minutes, tap B was turned on. At 11.13 p.m., the tank was half filled with water.
- How many litres of water flowed out of tap B in 1 minute?
- At 11.22 p.m., what fraction of the tank was filled with water?
(a)
Volume of the tank
= 60 x 35 x 30
= 63000 mℓ
= 63 ℓ
Volume of the tank at 11.13 p.m. when it was half filled with water
= 63 ÷ 2
= 31.5 ℓ
Volume of water by Tap A for 8 min
= 8 x 4.2
= 33.6 ℓ
Duration that Tap B was turned
= 13 - 8
= 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
= 33.6 - 31.5
= 2.1 ℓ
Volume of water that flowed out in 1 min
= 2.1 ÷ 5
= 0.42 ℓ
Volume of water that flowed out of Tap B in 1 min
= 4.2 + 0.42
= 4.62 ℓ
(b)
Duration from 11.13 p.m. to 11.22 p.m. = 9 min
Volume of water that flowed out from 11.13 p.m. to 11.22 p.m.
= 9 x 0.42
= 3.78 ℓ
Volume of water left at 11.22 p.m.
= 31.5 - 3.78
= 27.72 ℓ
Fraction of the tank filled with water at 11.22 p.m.
=
27.7263 =
1125
Answer(s): (a) 4.62 ℓ; (b) 1125