Water flows into a container through Tap Z and flows out of the container through Tap A. The capacity of a container is 54 litres. When only Tap Z is turned on, the container is completely filled in 14 minutes. When only Tap A 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 68% of the container?
2. How much water has flowed out through Tap A by the time the container is ⁴₅ filled with water?  Express your answer in litres.

(a)
Tap Z :
14 min → 1 container
1 min → ¹₁₄ container

¹₄ hour = ¹₄ x 60 = 15 min

Tap A:
15 min → 1 container
1 min → ¹₁₅ container

Tap Z and Tap A:
1 min → ¹₁₄ - ¹₁₅ = ¹⁵₂₁₀ - ¹⁴₂₁₀ = ¹₂₁₀ container
1 container → ²¹⁰₁ = 210 min

68% container → 68% x 210 = 142.8 min

(b)
Time taken to fill ⁴₅ of the container
1 container → 210 min
⁴₅ container → 210 x ⁴₅ = 168 min

Volume that flows out per min
= ¹₁₅ container
= ¹₁₅ x 54
= 3.6 ℓ 

Volume of water that flowed out through Tap A in 168 min
= 168 x 3.6
= 604.8 ℓ

Answer(s): (a) 142.8 min; (b) 604.8 ℓ