Water flows into a container through Tap X and flows out of the container through Tap Y. The capacity of a container is 54 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
14 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 58% of the container?
- How much water has flowed out through Tap Y by the time the container is 45 filled with water? Express your answer in litres.
(a)
Tap X :
12 min → 1 container
1 min →
112 container
14 hour =
14 x 60 = 15 min
Tap Y:
15 min → 1 container
1 min →
115 container
Tap X and Tap Y:
1 min →
112 -
115 =
560 -
460 =
160 container
1 container →
601 = 60 min
58% container → 58% x 60 = 34.8 min
(b)
Time taken to fill
45 of the container
1 container → 60 min
45 container → 60 x
45 = 48 min
Volume that flows out per min
=
115 container
=
115 x 54
= 3.6 ℓ
Volume of water that flowed out through Tap Y in 48 min
= 48 x 3.6
= 172.8 ℓ
Answer(s): (a) 34.8 min; (b) 172.8 ℓ