Water flows into a tank through Tap U and flows out of the container through Tap V. The capacity of a tank is 78 litres. When only Tap U is turned on, the container is completely filled in 12 minutes. When only Tap V 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 50% of the tank?
- How much water has flowed out through Tap V by the time the tank is 35 filled with water? Express your answer in litres.
(a)
Tap U :
12 min → 1 tank
1 min →
112 tank
12 hour =
12 x 60 = 30 min
Tap V:
30 min → 1 tank
1 min →
130 tank
Tap U and Tap V:
1 min →
112 -
130 =
560 -
260 =
120 tank
1 tank →
201 = 20 min
50% tank → 50% x 20 = 10 min
(b)
Time taken to fill
35 of the tank
1 tank → 20 min
35 tank → 20 x
35 = 12 min
Volume that flows out per min
=
130 tank
=
130 x 78
= 2.6 ℓ
Volume of water that flowed out through Tap V in 12 min
= 12 x 2.6
= 31.2 ℓ
Answer(s): (a) 10 min; (b) 31.2 ℓ