Water flows into a tank through Tap Q and flows out of the container through Tap R. The capacity of a tank is 42 litres. When only Tap Q is turned on, the container is completely filled in 14 minutes. When only Tap R 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 90% of the tank?
- How much water has flowed out through Tap R by the time the tank is 45 filled with water? Express your answer in litres.
(a)
Tap Q :
14 min → 1 tank
1 min →
114 tank
14 hour =
14 x 60 = 15 min
Tap R:
15 min → 1 tank
1 min →
115 tank
Tap Q and Tap R:
1 min →
114 -
115 =
15210 -
14210 =
1210 tank
1 tank →
2101 = 210 min
90% tank → 90% x 210 = 189 min
(b)
Time taken to fill
45 of the tank
1 tank → 210 min
45 tank → 210 x
45 = 168 min
Volume that flows out per min
=
115 tank
=
115 x 42
= 2.8 ℓ
Volume of water that flowed out through Tap R in 168 min
= 168 x 2.8
= 470.4 ℓ
Answer(s): (a) 189 min; (b) 470.4 ℓ