Water flows into a container through Tap X and flows out of the container through Tap Y. The capacity of a container is 78 litres. When only Tap X is turned on, the container is completely filled in 12 minutes. When only Tap Y 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 52% of the container?
- How much water has flowed out through Tap Y by the time the container is 35 filled with water? Express your answer in litres.
(a)
Tap X :
12 min → 1 container
1 min →
112 container
12 hour =
12 x 60 = 30 min
Tap Y:
30 min → 1 container
1 min →
130 container
Tap X and Tap Y:
1 min →
112 -
130 =
560 -
260 =
120 container
1 container →
201 = 20 min
52% container → 52% x 20 = 10.4 min
(b)
Time taken to fill
35 of the container
1 container → 20 min
35 container → 20 x
35 = 12 min
Volume that flows out per min
=
130 container
=
130 x 78
= 2.6 ℓ
Volume of water that flowed out through Tap Y in 12 min
= 12 x 2.6
= 31.2 ℓ
Answer(s): (a) 10.4 min; (b) 31.2 ℓ