Water flows into a container through Tap P and flows out of the container through Tap Q. The capacity of a container is 52 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
13 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 84% of the container?
- How much water has flowed out through Tap Q by the time the container is 35 filled with water? Express your answer in litres.
(a)
Tap P :
12 min → 1 container
1 min →
112 container
13 hour =
13 x 60 = 20 min
Tap Q:
20 min → 1 container
1 min →
120 container
Tap P and Tap Q:
1 min →
112 -
120 =
560 -
360 =
130 container
1 container →
301 = 30 min
84% container → 84% x 30 = 25.2 min
(b)
Time taken to fill
35 of the container
1 container → 30 min
35 container → 30 x
35 = 18 min
Volume that flows out per min
=
120 container
=
120 x 52
= 2.6 ℓ
Volume of water that flowed out through Tap Q in 18 min
= 18 x 2.6
= 46.8 ℓ
Answer(s): (a) 25.2 min; (b) 46.8 ℓ