PSLE The figure shows taps A and B and an empty tank. At 7 p.m., tap A was turned on. Water flowed into the tank from tap A at a rate of 4.5 litres per minute. After 4 minutes, tap B was turned on. At 7.14 p.m., the tank was half filled with water.
- How many litres of water flowed out of tap B in 1 minute?
- At 7.29 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 7.14 p.m. when it was half filled with water
= 27 ÷ 2
= 13.5 ℓ
Volume of water by Tap A for 4 min
= 4 x 4.5
= 18 ℓ
Duration that Tap B was turned
= 14 - 4
= 10 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 10 min
= 18 - 13.5
= 4.5 ℓ
Volume of water that flowed out in 1 min
= 4.5 ÷ 10
= 0.45 ℓ
Volume of water that flowed out of Tap B in 1 min
= 4.5 + 0.45
= 4.95 ℓ
(b)
Duration from 7.14 p.m. to 7.29 p.m. = 15 min
Volume of water that flowed out from 7.14 p.m. to 7.29 p.m.
= 15 x 0.45
= 6.75 ℓ
Volume of water left at 7.29 p.m.
= 13.5 - 6.75
= 6.75 ℓ
Fraction of the tank filled with water at 7.29 p.m.
=
6.7527 =
14
Answer(s): (a) 4.95 ℓ; (b) 14