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 2.7 litres per minute. After 7 minutes, tap B was turned on. At 3.15 p.m., the tank was half filled with water.
- How many litres of water flowed out of tap B in 1 minute?
- At 3.26 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 3.15 p.m. when it was half filled with water
= 27 ÷ 2
= 13.5 ℓ
Volume of water by Tap A for 7 min
= 7 x 2.7
= 18.9 ℓ
Duration that Tap B was turned
= 15 - 7
= 8 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 8 min
= 18.9 - 13.5
= 5.4 ℓ
Volume of water that flowed out in 1 min
= 5.4 ÷ 8
= 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 3.15 p.m. to 3.26 p.m. = 11 min
Volume of water that flowed out from 3.15 p.m. to 3.26 p.m.
= 11 x 0.675
= 7.425 ℓ
Volume of water left at 3.26 p.m.
= 13.5 - 7.425
= 6.075 ℓ
Fraction of the tank filled with water at 3.26 p.m.
=
6.07527 =
940
Answer(s): (a) 3.375 ℓ; (b) 940