Water flows into a tank through Tap W and flows out of the container through Tap X. The capacity of a tank is 70 litres. When only Tap W is turned on, the container is completely filled in 12 minutes. When only Tap X is turned on, it takes ¹₃ hour for all the water to flow out. If both taps are turned on at the same time,

1. How long does it take to fill 86% of the tank?
2. How much water has flowed out through Tap X by the time the tank is ³₅ filled with water?  Express your answer in litres.

(a)
Tap W :
12 min → 1 tank
1 min → ¹₁₂ tank

¹₃ hour = ¹₃ x 60 = 20 min

Tap X:
20 min → 1 tank
1 min → ¹₂₀ tank

Tap W and Tap X:
1 min → ¹₁₂ - ¹₂₀ = ⁵₆₀ - ³₆₀ = ¹₃₀ tank
1 tank → ³⁰₁ = 30 min

86% tank → 86% x 30 = 25.8 min

(b)
Time taken to fill ³₅ of the tank
1 tank → 30 min
³₅ tank → 30 x ³₅ = 18 min

Volume that flows out per min
= ¹₂₀ tank
= ¹₂₀ x 70
= 3.5 ℓ 

Volume of water that flowed out through Tap X in 18 min
= 18 x 3.5
= 63 ℓ

Answer(s): (a) 25.8 min; (b) 63 ℓ