Water flows into a tank through Tap S and flows out of the container through Tap T. The capacity of a tank is 60 litres. When only Tap S is turned on, the container is completely filled in 14 minutes. When only Tap T is turned on, it takes ¹₄ 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 34% of the tank?
2. How much water has flowed out through Tap T by the time the tank is ³₅ filled with water?  Express your answer in litres.

(a)
Tap S :
14 min → 1 tank
1 min → ¹₁₄ tank

¹₄ hour = ¹₄ x 60 = 15 min

Tap T:
15 min → 1 tank
1 min → ¹₁₅ tank

Tap S and Tap T:
1 min → ¹₁₄ - ¹₁₅ = ¹⁵₂₁₀ - ¹⁴₂₁₀ = ¹₂₁₀ tank
1 tank → ²¹⁰₁ = 210 min

34% tank → 34% x 210 = 71.4 min

(b)
Time taken to fill ³₅ of the tank
1 tank → 210 min
³₅ tank → 210 x ³₅ = 126 min

Volume that flows out per min
= ¹₁₅ tank
= ¹₁₅ x 60
= 4 ℓ 

Volume of water that flowed out through Tap T in 126 min
= 126 x 4
= 504 ℓ

Answer(s): (a) 71.4 min; (b) 504 ℓ