Water flows into a container through Tap R and flows out of the container through Tap S. The capacity of a container is 50 litres. When only Tap R is turned on, the container is completely filled in 16 minutes. When only Tap S 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 84% of the container?
2. How much water has flowed out through Tap S by the time the container is ²₅ filled with water?  Express your answer in litres.

(a)
Tap R :
16 min → 1 container
1 min → ¹₁₆ container

¹₃ hour = ¹₃ x 60 = 20 min

Tap S:
20 min → 1 container
1 min → ¹₂₀ container

Tap R and Tap S:
1 min → ¹₁₆ - ¹₂₀ = ⁵₈₀ - ⁴₈₀ = ¹₈₀ container
1 container → ⁸⁰₁ = 80 min

84% container → 84% x 80 = 67.2 min

(b)
Time taken to fill ²₅ of the container
1 container → 80 min
²₅ container → 80 x ²₅ = 32 min

Volume that flows out per min
= ¹₂₀ container
= ¹₂₀ x 50
= 2.5 ℓ 

Volume of water that flowed out through Tap S in 32 min
= 32 x 2.5
= 80 ℓ

Answer(s): (a) 67.2 min; (b) 80 ℓ