PSLE The figure shows taps A and B and an empty tank. At 2 p.m., tap A was turned on. Water flowed into the tank from tap A at a rate of 3.9 litres per minute. After 8 minutes, tap B was turned on. At 2.11 p.m., the tank was half filled with water.
- How many litres of water flowed out of tap B in 1 minute?
- At 2.26 p.m., what fraction of the tank was filled with water?
(a)
Volume of the tank
= 60 x 35 x 25
= 52500 mℓ
= 52.5 ℓ
Volume of the tank at 2.11 p.m. when it was half filled with water
= 52.5 ÷ 2
= 26.25 ℓ
Volume of water by Tap A for 8 min
= 8 x 3.9
= 31.2 ℓ
Duration that Tap B was turned
= 11 - 8
= 3 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 3 min
= 31.2 - 26.25
= 4.95 ℓ
Volume of water that flowed out in 1 min
= 4.95 ÷ 3
= 1.65 ℓ
Volume of water that flowed out of Tap B in 1 min
= 3.9 + 1.65
= 5.55 ℓ
(b)
Duration from 2.11 p.m. to 2.26 p.m. = 15 min
Volume of water that flowed out from 2.11 p.m. to 2.26 p.m.
= 15 x 1.65
= 24.75 ℓ
Volume of water left at 2.26 p.m.
= 26.25 - 24.75
= 1.5 ℓ
Fraction of the tank filled with water at 2.26 p.m.
=
1.552.5 =
135
Answer(s): (a) 5.55 ℓ; (b) 135