Water flows into a container through Tap P and flows out of the container through Tap Q. The capacity of a container is 78 litres. When only Tap P is turned on, the container is completely filled in 12 minutes. When only Tap Q is turned on, it takes
12 hour for all the water to flow out. If both taps are turned on at the same time,
- How long does it take to fill 44% of the container?
- How much water has flowed out through Tap Q by the time the container is 45 filled with water? Express your answer in litres.
(a)
Tap P :
12 min → 1 container
1 min →
112 container
12 hour =
12 x 60 = 30 min
Tap Q:
30 min → 1 container
1 min →
130 container
Tap P and Tap Q:
1 min →
112 -
130 =
560 -
260 =
120 container
1 container →
201 = 20 min
44% container → 44% x 20 = 8.8 min
(b)
Time taken to fill
45 of the container
1 container → 20 min
45 container → 20 x
45 = 16 min
Volume that flows out per min
=
130 container
=
130 x 78
= 2.6 ℓ
Volume of water that flowed out through Tap Q in 16 min
= 16 x 2.6
= 41.6 ℓ
Answer(s): (a) 8.8 min; (b) 41.6 ℓ