PSLE The figure shows taps A and B and an empty tank. At 10 p.m., tap A was turned on. Water flowed into the tank from tap A at a rate of 3.6 litres per minute. After 8 minutes, tap B was turned on. At 10.12 p.m., the tank was half filled with water.
- How many litres of water flowed out of tap B in 1 minute?
- At 10.24 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 10.12 p.m. when it was half filled with water
= 45 ÷ 2
= 22.5 ℓ
Volume of water by Tap A for 8 min
= 8 x 3.6
= 28.8 ℓ
Duration that Tap B was turned
= 12 - 8
= 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
= 28.8 - 22.5
= 6.3 ℓ
Volume of water that flowed out in 1 min
= 6.3 ÷ 4
= 1.575 ℓ
Volume of water that flowed out of Tap B in 1 min
= 3.6 + 1.575
= 5.175 ℓ
(b)
Duration from 10.12 p.m. to 10.24 p.m. = 12 min
Volume of water that flowed out from 10.12 p.m. to 10.24 p.m.
= 12 x 1.575
= 18.9 ℓ
Volume of water left at 10.24 p.m.
= 22.5 - 18.9
= 3.6 ℓ
Fraction of the tank filled with water at 10.24 p.m.
=
3.645 =
225
Answer(s): (a) 5.175 ℓ; (b) 225